ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Robust Exponential Stability of Impulsive Stochastic Neural Networks with Markovian Switching and Mixed Time-varying Delays

Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 427--446 | DOI:10.5890/DNC.2016.12.008

Haoru Li$^{1}$, Yang Fang$^{2}$, Kelin Li$^{2}$

$^{1}$ School of Automation and Electronic Information, Sichuan University of Science & Engineering, Sichuan 643000, P.R. China

$^{2}$ School of Science, Sichuan University of Science & Engineering, Sichuan 643000, P.R. China

Abstract

This paper is concerned with the robust exponential stability problem for a class of impulsive stochastic neural networks with Markovian switching, mixed time-varying delays and parametric uncertainties. By construct a novel Lyapunov-Krasovskii functional, and using linear matrix inequality (LMI) technique, Jensen integral inequality and free-weight matrix method, several novel sufficient conditions in the form of LMIs are derived to ensure the robust exponential stability in mean square of the trivial solution of the considered system. The results obtained in this paper improve many known results, since the parametric uncertainties have been taken into account, and the derivatives of discrete and distributed time-varying delays need not to be 0 or smaller than 1. Finally, three illustrative examples are given to show the effectiveness of the proposed method.

Acknowledgments

This work was supported by the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing under Grants No. 2014QZJ01 and No. 2015QYJ01, National Natural Science Foundation of China under Grant 61573010.

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