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Zbl 1221.93265
Raja, Ramachandran; Sakthivel, Rathinasamy; Marshal Anthoni, Selvaraj; Kim, Hyunsoo
Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays. (English)
[J] Int. J. Appl. Math. Comput. Sci. 21, No. 1, 127-135 (2011). ISSN 1641-876X

Summary: The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the {\tt Matlab} LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

MSC 2000:: *93E15 Stochastic stability
60J75 Jump processes
92B20 General theory of neural networks

Keywords: Hopfield neural networks; Markovian jumping; stochastic stability; Lyapunov function; impulses

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