Shouming Zhong

Publications

41 Globally Exponential Stability and Dissipativity Analysis of Static Neural Networks with Time Delay

Authors: Shouming Zhong, Yucai Ding, Lijiang Xiang

Abstract:

The problems of globally exponential stability and dissipativity analysis for static neural networks (NNs) with time delay is investigated in this paper. Some delay-dependent stability criteria are established for static NNs with time delay using the delay partitioning technique. In terms of this criteria, the delay-dependent sufficient condition is given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Two numerical examples are used to show the effectiveness of the proposed methods.

Keywords: Time Delay, globally exponential stability, Dissipativity, Static neural networks

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40 Reachable Set Bounding Estimation for Distributed Delay Systems with Disturbances

Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: distributed delay, Reachable set, Lyapunov-Krasovskii function, Polytopic uncertainties

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39 Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Authors: Shouming Zhong, Qingqing Wang

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural Networks, Globally asymptotic stability, LMI approach, Additive time-varying delays

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38 Delay-Dependent Stability Analysis for Neutral Type Neural Networks with Uncertain Parameters and Time-Varying Delay

Authors: Shouming Zhong, Qingqing Wang

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Stability, Neutral type neural networks, Time-varying delay, Linear matrix inequality(LMI)

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37 Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

Authors: Shouming Zhong, Liyuan Wang

Abstract:

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

Keywords: Neural Networks, globally exponential stability, State estimator

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36 Delay-Dependent Stability Analysis for Neural Networks with Distributed Delays

Authors: Shouming Zhong, Qingqing Wang

Abstract:

This paper deals with the problem of delay-dependent stability for neural networks with distributed delays. Some new sufficient condition are derived by constructing a novel Lyapunov-Krasovskii functional approach. The criteria are formulated in terms of a set of linear matrix inequalities, this is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Moreover, in order to show the stability condition in this paper gives much less conservative results than those in the literature, numerical examples are considered.

Keywords: Neural Networks, distributed delays, Globally asymptotic stability, LMI approach

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35 New Approaches on Stability Analysis for Neural Networks with Time-Varying Delay

Authors: Shouming Zhong, Qingqing Wang

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural Networks, Time-varying delay, Globally asymptotic stability, LMI approach, IIA approach

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34 Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delays

Authors: Shouming Zhong, Miaomiao Yang

Abstract:

This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Neural Networks, Stability, lyapunov function, time-varying delays, Linear Matrix Inequalities (LMI)

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33 New Stability Analysis for Neural Networks with Time-Varying Delays

Authors: Shouming Zhong, Miaomiao Yang

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural Networks, time-varying delays, linear matrix inequality, Lyapunov-Krasovskii

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32 Stability Analysis of Neural Networks with Leakage, Discrete and Distributed Delays

Authors: Shouming Zhong, Qingqing Wang, Baocheng Chen

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural Networks, Stability, time-varying delays, linear matrix inequality

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31 Exponential Stability Analysis for Uncertain Neural Networks with Discrete and Distributed Time-Varying Delays

Authors: Shouming Zhong, Miaomiao Yang

Abstract:

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: exponential stability, time-varying, LMI approach, Uncertain Neural networks, Lyapunov-Krasovskii function

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30 Stability Criteria for Uncertainty Markovian Jumping Parameters of BAM Neural Networks with Leakage and Discrete Delays

Authors: Shouming Zhong, Qingqing Wang, Baocheng Chen

Abstract:

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, linear matrix inequality, Markovian jumping neural networks, Timevarying delays

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29 Asymptotic Properties of a Stochastic Predator-Prey Model with Bedding-DeAngelis Functional Response

Authors: Shouming Zhong, Xianqing Liu, Lijiang Xiang

Abstract:

In this paper, a stochastic predator-prey system with Bedding-DeAngelis functional response is studied. By constructing a suitable Lyapunov founction, sufficient conditions for species to be stochastically permanent is established. Meanwhile, we show that the species will become extinct with probability one if the noise is sufficiently large.

Keywords: white noise, extinct, Stochastically permanent, Bedding-DeAngelis functional response

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28 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

Authors: Shouming Zhong, Chuanyun Gu

Abstract:

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

Keywords: boundary value problem, positive solution, Fractional differential equation, existence and uniqueness, Fixed point theorem of a sum operator

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27 Improved Exponential Stability Analysis for Delayed Recurrent Neural Networks

Authors: Shouming Zhong, Miaomiao Yang

Abstract:

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Neural Networks, linear matrix inequality, exponential stability, Lyapunov-Krasovskii, time-varying

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26 New Approaches on Exponential Stability Analysis for Neural Networks with Time-Varying Delays

Authors: Shouming Zhong, Qingqing Wang, Baocheng Chen

Abstract:

In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural Networks, time-varying delays, exponential stability, LMI approach

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25 Exponential Passivity Criteria for BAM Neural Networks with Time-Varying Delays

Authors: Shouming Zhong, Qingqing Wang, Baocheng Chen

Abstract:

In this paper,the exponential passivity criteria for BAM neural networks with time-varying delays is studied.By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments,a novel sufficient condition is established to guarantee the exponential stability of the considered system.Finally,a numerical example is provided to illustrate the usefulness of the proposed main results

Keywords: time-varying delays, BAM neural networks, LMI approach, Exponential passivity

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24 Properties of a Stochastic Predator-Prey System with Holling II Functional Response

Authors: Shouming Zhong, Xianqing Liu, Fuli Zhong, Zijian Liu

Abstract:

In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, some simulation figures are carried out to support the analytical findings.

Keywords: white noise, global stability, Markovian switching, stochastically bounded, Holling II functional response

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23 A New Robust Stability Criterion for Dynamical Neural Networks with Mixed Time Delays

Authors: Guang Zhou, Shouming Zhong

Abstract:

In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.

Keywords: Neural Networks, Stability Analysis, lyapunov function, delayed systems

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22 Robust Stability Criteria for Uncertain Genetic Regulatory Networks with Time-Varying Delays

Authors: Wenqin Wang, Shouming Zhong

Abstract:

This paper presents the robust stability criteria for uncertain genetic regulatory networks with time-varying delays. One key point of the criterion is that the decomposition of the matrix ˜D into ˜D = ˜D1 + ˜D2. This decomposition corresponds to a decomposition of the delayed terms into two groups: the stabilizing ones and the destabilizing ones. This technique enables one to take the stabilizing effect of part of the delayed terms into account. Meanwhile, by choosing an appropriate new Lyapunov functional, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Keywords: lyapunov-krasovskii functional, Time-varying delay, Genetic regulatory network, Uncertain system

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21 Augmented Lyapunov Approach to Robust Stability of Discrete-time Stochastic Neural Networks with Time-varying Delays

Authors: Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Keywords: stochastic, time-varying delays, Robust exponential stability, delay-dependent stability, discrete-time neural networks

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20 Novel Delay-Dependent Stability Criteria for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delays

Authors: Shouming Zhong, Mengzhuo Luo

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Neural Networks, linear matrix inequality (LMI), time varying delay, delay-dependent stability

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19 New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components

Authors: Shouming Zhong, Xingyuan Qu

Abstract:

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: time-varying delays, linear matrix inequality (LMI), lyapunov functional, delay-dependent stability

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18 Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

Authors: Xiuyong Ding, Shouming Zhong, Xiu Liu

Abstract:

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

Keywords: Switched Systems, Robust Stabilization, Impulsive systems, quadratic stabilization

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17 On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays

Authors: Xiuyong Ding, Shouming Zhong, Xiu Liu

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Switched Systems, delays, Common linear co-positive Lyapunov functions, positive systems

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16 Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay

Authors: Shouming Zhong, Liqiong Liu

Abstract:

In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.

Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality

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15 Time Series Forecasting Using a Hybrid RBF Neural Network and AR Model Based On Binomial Smoothing

Authors: Shouming Zhong, Fengxia Zheng

Abstract:

ANNARIMA that combines both autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models. This paper provides a hybrid methodology that combines both radial basis function (RBF) neural network and auto regression (AR) model based on binomial smoothing (BS) technique which is efficient in data processing, which is called BSRBFAR. This method is examined by using the data of Canadian Lynx data. Empirical results indicate that the over-fitting problem can be eased using RBF neural network based on binomial smoothing which is called BS-RBF, and the hybrid model–BS-RBFAR can be an effective way to improve forecasting accuracy achieved by BSRBF used separately.

Keywords: Hybrid, Forecasting Accuracy, Binomial smoothing (BS), Canadian Lynx data

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14 Delay-Dependent H∞ Performance Analysis for Markovian Jump Systems with Time-Varying Delays

Authors: Shouming Zhong, Yucai Ding, Hong Zhu, Yuping Zhang

Abstract:

This paper considers ­H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed ­H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.

Keywords: linear matrix inequality (LMI), Markovian switching, ­H∞ performance, Delaydependent stability

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13 Robust BIBO Stabilization Analysis for Discrete-time Uncertain System

Authors: Mao Ye, Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.

Keywords: Time Delay, discrete-time system, Robust BIBO stabilization, delay-dependent stabilization

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12 On a New Nonlinear Sum-difference Inequality with Application

Authors: Shouming Zhong, Kelong Zheng

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Nonlinear, boundedness, Sum-Difference inequality

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11 New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations

Authors: Xiuyong Ding, Shouming Zhong, Lianglin Xiong

Abstract:

In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: linear matrix inequality (LMI), asymptotical stability, nonlinear perturbation, Neutral system, delay-dependent

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10 Improved Robust Stability Criteria for Discrete-time Neural Networks

Authors: Mao Ye, Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: time-varying delays, Robust exponential stability, delay-dependent stability, discrete-time neutral networks

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9 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching

Authors: Shouming Zhong, Xia Zhou

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, Markov Chain, Brownian motion, M-matrix, delay-range-dependent, generalized Itō's formula

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8 Improved Asymptotic Stability Criteria for Uncertain Neutral Systems with Time-varying Discrete Delays

Authors: Shouming Zhong, Changchun Shen

Abstract:

This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Stability, Lyapunov, linear matrix inequalities, Neutral system

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7 Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses

Authors: Shouming Zhong, Xiaomei Wang

Abstract:

In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Equilibrium, existence, mixed delays, globally exponential stability, Bi-directional associative memory (BAM) neural networks, Lyapunov stability theory, contraction mapping theorem

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6 Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays

Authors: Shouming Zhong, Changchun Shen

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Stability, Lyapunov, linear matrix inequalities, Lur'e system

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5 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

Authors: Mao Ye, Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays

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4 Delay-dependent Stability Analysis for Uncertain Switched Neutral System

Authors: Mao Ye, Shouming Zhong, Lianglin Xiong

Abstract:

This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

Keywords: exponential stability, Switched neutral system, multiple Lyapunov functional, dwell time technique, time-dependent switching rule

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3 pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors: Mao Ye, Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: Neural Networks, stochastic, pth Moment Exponential synchronization, Mixed time delays

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2 New Stabilization for Switched Neutral Systems with Perturbations

Authors: Mao Ye, Shouming Zhong, Lianglin Xiong

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: nonlinear perturbation, Switched neutral system, piecewise Lyapunov functional, Lyapunov-Metzler linear matrix inequality

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1 Exponential Stability and Periodicity of a Class of Cellular Neural Networks with Time-Varying Delays

Authors: Mao Ye, Zixin Liu, Shu Lü, Shouming Zhong

Abstract:

The problem of exponential stability and periodicity for a class of cellular neural networks (DCNNs) with time-varying delays is investigated. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via the methods of variation parameters and inequality techniques. These conditions are represented by some blocks of the interconnection matrices. Compared with some previous methods, the method used in this paper does not resort to any Lyapunov function, and the results derived in this paper improve and generalize some earlier criteria established in the literature cited therein. Two examples are discussed to illustrate the main results.

Keywords: exponential stability, periodic solution, Cellular neural networks, time varying delays, partitioned matrices

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Abstracts

1 Anti-Phase Synchronization of Complex Delayed Networks with Output Coupling via Pinning Control

Authors: Shouming Zhong, Chanyuan Gu

Abstract:

Synchronization is a fundamental phenomenon that enables coherent behavior in networks as a result of interactions. The purpose of this research had been to investigate the problem of anti-phase synchronization for complex delayed dynamical networks with output coupling. The coupling configuration is general, with the coupling matrix not assumed to be symmetric or irreducible. The amount of the coupling variables between two connected nodes is flexible, the nodes in the drive and response systems need not to be identical and there is not any extra constraint on the coupling matrix. Some pinning controllers are designed to make the drive-response system achieve the anti-phase synchronization. For the convenience of description, we applied the matrix Kronecker product. Some new criteria are proposed based on the Lyapunov stability theory, linear matrix inequalities (LMI) and Schur complement. Lastly, some simulation examples are provided to illustrate the effectiveness of our proposed conditions.

Keywords: Complex Networks, anti-phase synchronization, output coupling, pinning control

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