Publications
13 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays
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: exponential stability, Lur’e system, Convex function, Jensen integral inequality, Triple-integral method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 121212 Augmented Lyapunov Approach to Robust Stability of Discrete-time Stochastic Neural Networks with Time-varying Delays
Authors: Shu Lü, Shouming Zhong, Zixin Liu
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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 118711 Modeling and Stability Analysis of Delayed Game Network
Authors: Zixin Liu, Jian Yu, Daoyun Xu
Abstract:
This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.
Keywords: Time Delay, Game networks, zero-sum game, delayed singular system, nonlinear perturbation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 114310 New PTH Moment Stable Criteria of Stochastic Neural Networks
Authors: Zixin Liu, Huawei Yang, Fangwei Chen
Abstract:
In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.
Keywords: Neural Networks, stochastic, time varying delays, distributed delays, PTH moment stable
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11839 Mean Square Exponential Synchronization of Stochastic Neutral Type Chaotic Neural Networks with Mixed Delay
Authors: Zixin Liu, Huawei Yang, Fangwei Chen
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This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.
Keywords: Stochastic Analysis, Exponential synchronization, chaotic neural networks, neutral type system
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12768 Robust BIBO Stabilization Analysis for Discrete-time Uncertain System
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12677 Exponential Stability Analysis for Switched Cellular Neural Networks with Time-varying Delays and Impulsive Effects
Authors: Zixin Liu, Fangwei Chen
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10966 PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays
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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9325 Improved Robust Stability Criteria for Discrete-time Neural Networks
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12004 Improved Robust Stability and Stabilization Conditions of Discrete-time Delayed System
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 Stability, Robust Stabilization, Time Delay, discrete-time system
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12273 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17012 pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12831 Exponential Stability and Periodicity of a Class of Cellular Neural Networks with Time-Varying Delays
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1241