Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

N Mala,A R Sudamani Ramaswamy

doi:10.1155/2013/172906

Abstract

This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.

Highlights

In the past few decades, neural networks (NNs) have been a hot research topic because of their emerged application in static image processing, pattern recognition, fixed-point computation, associative memory, combinatorial optimization [1,2,3,4,5]
Since the existence of time delays is frequently one of the main sources of instability for neural networks, the stability analysis for delayed neural networks had been extensively studied and many papers have been published on various types of neural networks with time delays based on the linear matrix inequalities (LMIs) approach [6,7,8,9,10,11,12,13,14]
With reference to the results above, it has been studied that many results get to be found out for passivity analysis of Markovian jumping neural networks with leakage time-varying delays

Summary

Introduction

In the past few decades, neural networks (NNs) have been a hot research topic because of their emerged application in static image processing, pattern recognition, fixed-point computation, associative memory, combinatorial optimization [1,2,3,4,5]. The passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term have been addressed in [37]. With reference to the results above, it has been studied that many results get to be found out for passivity analysis of Markovian jumping neural networks with leakage time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple integral terms, new passivity leakage delaydependent criteria are established to guarantee the passivity performance of the given systems. This performance depends on the upper bound of the time-varying leakage delay σ(t) and depends on the upper bound of the derivative of the time-varying leakage delay σμ.

Problem Description and Preliminaries

Main Results

Problem without Switching

Numerical Examples

Conclusion