A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

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.

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Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2010/810408 ◽

2010 ◽

Vol 2010 ◽

pp. 1-19 ◽

Cited By ~ 12

Author(s):

Qiankun Song ◽

Jinde Cao

Keyword(s):

Neural Networks ◽

Linear Matrix Inequality ◽

Discrete Time ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequality ◽

Computationally Efficient ◽

Inequality Technique ◽

General Activation ◽

Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

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A New Result on Stability Analysis of Recurrent Neural Networks with Time-Varying Delay Based on an Extended Delay-Dependent Integral Inequality

Neural Processing Letters ◽

10.1007/s11063-021-10601-y ◽

2021 ◽

Author(s):

Guoqiang Tan ◽

Zhanshan Wang

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Recurrent Neural Networks ◽

Integral Inequality ◽

Time Varying ◽

Time Varying Delay ◽

Delay Dependent ◽

Varying Delay

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Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

Abstract and Applied Analysis ◽

10.1155/2013/814692 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 7

Author(s):

M. J. Park ◽

O. M. Kwon ◽

Ju H. Park ◽

S. M. Lee ◽

E. J. Cha

Keyword(s):

Neural Networks ◽

Discrete Time ◽

Linear Matrix ◽

Time Varying ◽

Parameter Uncertainties ◽

Leakage Term ◽

Interval Time ◽

Robust Synchronization ◽

Delay Dependent ◽

Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

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