Complexity

Volume 20, Issue 3 p. 39-65

Research Article

Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

R. Rakkiyappan,

R. Rakkiyappan

Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, 641 046 India

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A. Chandrasekar,

A. Chandrasekar

Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, 641 046 India

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S. Lakshmanan,

S. Lakshmanan

Department of Mathematics, College of Science, UAE University, Al Ain, 15551 UAE

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Ju H. Park,

Corresponding Author

Ju H. Park

Department of Electrical Engineering, Yeungnam University, Kyongsan, 712-749 Republic of Korea

Correspondence to: Ju H. Park. E-mail: [email protected]Search for more papers by this author

R. Rakkiyappan,

R. Rakkiyappan

Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, 641 046 India

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A. Chandrasekar,

A. Chandrasekar

Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, 641 046 India

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S. Lakshmanan,

S. Lakshmanan

Department of Mathematics, College of Science, UAE University, Al Ain, 15551 UAE

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Ju H. Park,

Corresponding Author

Ju H. Park

Department of Electrical Engineering, Yeungnam University, Kyongsan, 712-749 Republic of Korea

Correspondence to: Ju H. Park. E-mail: [email protected]Search for more papers by this author

First published: 07 February 2014

https://doi.org/10.1002/cplx.21503

Citations: 36

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Abstract

In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015

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Volume20, Issue3

January/February 2015

Pages 39-65

Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract

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Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract

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