Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays

Authors:
Zheng-Guang Wu;Peng Shi;Hongye Su;Jian Chu
Affiliations:
National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, U.K.;National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China;National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China
Venue:
IEEE Transactions on Neural Networks
Year:
2011

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Abstract

In this paper, passivity analysis is conducted for discrete-time stochastic neural networks with both Markovian jumping parameters and mixed time delays. The mixed time delays consist of both discrete and distributed delays. The Markov chain in the underlying neural networks is finite piecewise homogeneous. By introducing a Lyapunov functional that accounts for the mixed time delays, a delay-dependent passivity condition is derived in terms of the linear matrix inequality approach. The case of Markov chain with partially unknown transition probabilities is also considered. All the results presented depend upon not only discrete delay but also distributed delay. A numerical example is included to demonstrate the effectiveness of the proposed methods.