Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays

Ling Hou,Dongyan Chen,Chan He

doi:10.1155/2019/5748923

Ling Hou, Dongyan Chen + Show 1 more

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https://doi.org/10.1155/2019/5748923

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Abstract

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

Highlights

neural networks (NNS) are a complex network system formed by a large number of simple processing units connected with each other
This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discretetime neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays
In [15], the passivity problem of Markov jump NNS was discussed by using linear matrix inequality (LMI) technique

Summary

Introduction

NNS are a complex network system formed by a large number of simple processing units connected with each other. Summarizing the discussions made so far, stochastic finite-time nonfragile dissipative control problem for discrete-time NNS contain Markovian jumps and mixed delays has not yet been investigated, which remains a good challenge. This kind of system model can be used to solve water pollution problems; see [32]. The objective of this paper is to study the problem of SFTD analysis based on nonfragile controller for a class of discrete time NNS with Markovian jumps and mixed delays. Diag{⋅} denotes the block diagonal matrix. ∗ denotes symmetry terms in a symmetric matrix, and MT denotes the transposition of matrix M

Problem Formulation and Preliminaries

Main Result

Numerical Examples

Conclusions

Conflicts of Interest