Improved stability analysis for Markovian Jump Static Neural Networks with Mode-Dependent Time-Varying Delays

Shyamsundarraj N,Sriraman R,Samidurai R

doi:10.26524/cm58

Abstract

This paper investigates the problem of delay-dependent stability analysis for Markovian jump static neural networks (MJSNNs) with mode-dependent time-varying delays. The fundamental objective of this paper is to create novel stability criterion for the considered MJSNNs with less conservatism. A suitable Lyapunov-Krasovskii functional (LKF) is constructed with more system information. By employing integral inequality, a novel delay-dependent sufficient condition is obtained to ensure the asymptotically stability of the equilibrium point. The obtained stability condition is derived and entrenched in terms of linear matrix inequality (LMI) which can be clearly checked by MATLAB LMI control toolbox. At long last, two benchmark illustrative case are given to show the effectiveness of the theoretical result.

Highlights

Over the past few decades, MJNNs have been broadly investigated
In the view of mathematical point, MJNNs can be regarded as a special class of stochastic neural networks with system matrices changed randomly at discrete time instances governed by a Markov process
In [3], delay-dependent stability analysis for Markovian jump static neural networks (MJSNNs) including the relative information on the interval time-varying delay is considered into the framework and derived delay-dependent sufficient conditions are expressed in the form of linear matrix inequality (LMI)

Summary

Introduction

Over the past few decades, MJNNs have been broadly investigated. The reason is mostly that MJNNs is a suitable scientific model to represent a class of dynamic systems subject to arbitrary unexpected changes in their structures, and discovered their applications in numerous areas, such as target tracking problems, fault-tolerant systems, manufactory processes and so on [1], [2]. To develop a novel integral inequality for quadratic functions plays a significant role in the issue of stability of NNs. Recently, various effective integral inequalities have been introduced to pick up an improved stability conditions, for example [22], [23], [24], [25], [26], and reference therein. In [3], delay-dependent stability analysis for MJSNNs including the relative information on the interval time-varying delay is considered into the framework and derived delay-dependent sufficient conditions are expressed in the form of LMIs. some various stability results have been examined in the recent works [4], [6]. Motivated by the above discussions, in this paper, our research efforts are mainly focused on developing a new approach to analyze the stability MJSNNs with mode-dependent time-varying delays.

Problem formulation and preliminaries

Stability Analysis

Illustrative Examples

Conclusion