Search results for: Lyapunov Stability.

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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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Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.

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Authors: Qingqing Wang, Shouming Zhong

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

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Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: Fangfang Meng, Shuang Cong

Abstract:

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

Keywords: Implicit Lyapunov control, state error, degenerate cases, convergence.

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Authors: Sun Lim, Il-Kyun Jung

Abstract:

This paper describes a newly designed decentralized nonlinear control strategy to control a robot manipulator. Based on the concept of the nonlinear state feedback theory and decentralized concept is developed to improve the drawbacks in previous works concerned with complicate intelligent control and low cost effective sensor. The control methodology is derived in the sense of Lyapunov theorem so that the stability of the control system is guaranteed. The decentralized algorithm does not require other joint angle and velocity information. Individual Joint controller is implemented using a digital processor with nearly actuator to make it possible to achieve good dynamics and modular. Computer simulation result has been conducted to validate the effectiveness of the proposed control scheme under the occurrence of possible uncertainties and different reference trajectories. The merit of the proposed control system is indicated in comparison with a classical control system.

Keywords: Robot manipulator control, nonlinear controller, Lyapunov based stability, Interconnection compensation.

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Authors: Mengzhuo Luo, Shouming Zhong

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: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee

Abstract:

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.

Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.

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Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva

Abstract:

In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.

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Authors: Zeynep Orman, Sabri Arik

Abstract:

This paper presents a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters of the neural system independently of the delay parameters. The results are also compared with the previously reported results in the literature.

Keywords: Equilibrium and stability analysis, Cohen-Grossberg Neural Networks, Lyapunov Functionals.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: K. Kamalanand, P. Mannar Jawahar

Abstract:

Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic systems. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using unscented transformation is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.

Keywords: Lyapunov exponents, unscented transformation, chaos theory, neural networks.

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Authors: Li Feng

Abstract:

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.

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Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

Abstract:

In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

Abstract:

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Zixin Liu, Fangwei Chen

Abstract:

In this Letter, a class of impulsive switched cellular neural networks with time-varying delays is investigated. At the same time, parametric uncertainties assumed to be norm bounded are considered. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions guaranteeing exponential stability for all admissible parametric uncertainties are derived via constructing appropriate Lyapunov functional. One numerical example is provided to illustrate the validity of the main results obtained in this paper.

Keywords: Switched systems, exponential stability, cellular neural networks.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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

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

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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

Abstract:

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Elif Derya UBEYLI, Inan GULER

Abstract:

A new approach based on the consideration that electroencephalogram (EEG) signals are chaotic signals was presented for automated diagnosis of electroencephalographic changes. This consideration was tested successfully using the nonlinear dynamics tools, like the computation of Lyapunov exponents. This paper presented the usage of statistics over the set of the Lyapunov exponents in order to reduce the dimensionality of the extracted feature vectors. Since classification is more accurate when the pattern is simplified through representation by important features, feature extraction and selection play an important role in classifying systems such as neural networks. Multilayer perceptron neural network (MLPNN) architectures were formulated and used as basis for detection of electroencephalographic changes. Three types of EEG signals (EEG signals recorded from healthy volunteers with eyes open, epilepsy patients in the epileptogenic zone during a seizure-free interval, and epilepsy patients during epileptic seizures) were classified. The selected Lyapunov exponents of the EEG signals were used as inputs of the MLPNN trained with Levenberg- Marquardt algorithm. The classification results confirmed that the proposed MLPNN has potential in detecting the electroencephalographic changes.

Keywords: Chaotic signal, Electroencephalogram (EEG) signals, Feature extraction/selection, Lyapunov exponents

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Authors: Meng Hu, Lili Wang

Abstract:

By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.

Keywords: Anti-periodic solution, coincidence degree, CGSICNNs, impulse, time scales.

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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

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: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

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Authors: Yucai Ding, Hong Zhu, Shouming Zhong, 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: ­H∞ performance, Markovian switching, Delaydependent stability, Linear matrix inequality (LMI)

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Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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