scholarly journals New Improved Exponential Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-23 ◽  
Author(s):  
Zixin Liu ◽  
Shu Lv ◽  
Shouming Zhong ◽  
Mao Ye
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Connection Weight ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Varying Delay

The robust stability of uncertain discrete-time recurrent neural networks with time-varying delay is investigated. By decomposing some connection weight matrices, new Lyapunov-Krasovskii functionals are constructed, and serial new improved stability criteria are derived. These criteria are formulated in the forms of linear matrix inequalities (LMIs). Compared with some previous results, the new results are less conservative. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Activation Functions ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

The problem of exponential stabilization of neutral-type neural networks with various activation functions and interval nondifferentiable and distributed time-varying delays is considered. The interval time-varying delay function is not required to be differentiable. By employing new and improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, the stabilizability criteria are formulated in terms of a linear matrix inequalities. Numerical examples are given to illustrate and show the effectiveness of the obtained results.

Stability analysis for discrete-time neural networks with time-varying delays and stochastic parameter uncertainties

2015 ◽  
Vol 93 (4) ◽  
pp. 398-408 ◽  
Author(s):  
O.M. Kwon ◽  
M.J. Park ◽  
S.M. Lee ◽  
E.J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Stochastic Parameter ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper proposes new delay-dependent stability criteria for discrete-time neural networks with interval time-varying delays and probabilistic occurring parameter uncertainties. It is assumed that parameter uncertainties are changed with the environment, explored using random situations, and its stochastic information is included in the proposed method. By constructing a suitable Lyapunov–Krasovskii functional, new delay-dependent stability criteria for the concerned systems are established in terms of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

2021 ◽  
Vol 20 ◽  
pp. 88-97
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

New Delay-Dependent Stability Criteria for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 48-49 ◽  
pp. 734-739 ◽  
Author(s):  
Dong Sheng Xu ◽  
Jun Kang Tian
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Integral Term ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for systems with interval time varying delay. By defining a new Lyapunov functional which contains a triple-integral term with the idea of decomposing the delay interval of time-varying delay, an improved criterion of asymptotic stability is derived in term of linear matrix inequalities. The criterion proves to be less conservative with fewer matrix variables than some previous ones. Finally, a numerical example is given to show the effectiveness of the proposed method.

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