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Z. Naturforsch. 69a, 70 – 80
(2014)
doi:10.5560/ZNA.2013-0078
Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay
1 National Laboratory of Industrial Control Technology, Institute of Cyber-System and Control, Zhejiang University, Yuquan Campus, Hangzhou 310027, China
2 Department of Mathematics, Sungkyunkwan University, Suwon-440 746, South Korea
3 Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore-641 010, India
Received May 17, 2013 / revised September 18, 2013 / published online December 18, 2013
Reprint requests to: S. R; E-mail:
krsakthivel@yahoo.com
This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.
Key words: Discrete-Time Neural Networks; Stochastic Stability; Leakage Delays; Linear Matrix Inequality; Markovian Jump Systems.