Shu Lü

Publications

7 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

Authors: Zixin Liu, Shu Lü, Longqiao Zhou

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

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6 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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5 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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4 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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3 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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2 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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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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