Dissipativity and passivity analysis of Markovian jump impulsive neural networks with time delays

ABSTRACT

This paper discusses the issue of dissipativity and passivity analysis for a class of impulsive neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modelled as a continuous-time discrete-state Markov chain. Based on a multiple integral inequality technique, a novel delay-dependent dissipativity criterion is established via a suitable Lyapunov functional involving the multiple integral terms. The proposed dissipativity and passivity conditions for the impulsive neural networks are represented by means of linear matrix inequalities. Finally, three numerical examples are given to show the effectiveness of the proposed criteria.

KEYWORDS:

• Dissipativity
• linear matrix inequality
• Lyapunov method
• Markovian jump parameters
• impulsive neural networks

2010 AMS SUBJECT CLASSIFICATIONS:

• 34A34
• 34D23
• 92B20
• 34K36
• 34K20

Acknowledgments

The authors are very thankful to the editors and anonymous reviewers for their careful reading, constructive comments and fruitful suggestions to improve this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the University Grants Commission – Basic Science Research (UGC – BSR) – Research fellowship in Mathematical Sciences – 2013–2014, Govt. of India, New Delhi.