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

Rakkiyappan, R., Chandrasekar, A., Lakshmanan, S. and Park, J. H. 2015, Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control, Complexity, vol. 20, no. 3, pp. 39-65, doi: 10.1002/cplx.21503.

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Title Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control
Author(s) Rakkiyappan, R.
Chandrasekar, A.
Lakshmanan, S.ORCID iD for Lakshmanan, S. orcid.org/0000-0002-4622-3782
Park, J. H.
Journal name Complexity
Volume number 20
Issue number 3
Start page 39
End page 65
Total pages 27
Publisher Wiley
Place of publication Weinheim, Germany
Publication date 2015-01-02
ISSN 1099-0526
1076-2787
Keyword(s) bidirectional associative memory neural networks
global exponential stability
Markovian jumping parameters
Probabilistic time-varying delays
Summary 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.
Language eng
DOI 10.1002/cplx.21503
Field of Research 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Wiley
Persistent URL http://hdl.handle.net/10536/DRO/DU:30077141

Document type: Journal Article
Collection: Centre for Intelligent Systems Research
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