New criteria for stability of generalized neural networks including markov jump parameters and additive time delays

R. Samidurai, R. Manivannan, Choon Ki Ahn, Hamid Reza Karimi

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

This paper examines the problem of asymptotic stability criteria for Markovian jump generalized neural networks with successive time-varying delay components. Generalized neural networks consist of a finite number of modes, which may jump from one mode to another according to a Markovian chain with known transition probability. By constructing novel augmented Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more and more information on the state vectors of the NNs, the upper bound of the successive time-varying delays is formulated. By employing a new integral inequality technique, free-weighting matrix-based integral inequality approach, and Wirtinger double integral inequality technique and that is combined with the reciprocally convex combination approach to estimate the single and double integral terms in the time derivative of the LKFs, a new set of delay-dependent conditions for the asymptotic stability of the considered NNs are represented in the form of linear matrix inequalities. Finally, five numerical examples are given to verify the effectiveness of the proposed approach with a four-tank benchmark real-world problem.

Original languageEnglish
Pages (from-to)485-499
Number of pages15
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Volume48
Issue number4
DOIs
Publication statusPublished - 2018 Apr 1

Keywords

  • Additive time delays
  • asymptotic stability
  • four-tank benchmark
  • generalized neural networks (NNs)
  • Markov jump parameters

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

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