Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control

• Published in: Neurocomputing (Amsterdam) Vol. 136; pp. 136 - 151
• Main Authors: Zhu, Quanxin, Rakkiyappan, R., Chandrasekar, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 20.07.2014; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer simulation; Connectionism. Neural networks; Delay; Exact sciences and technology; Global exponential stability; Impulse control; Leakage; Leakage delays; Lyapunov–Krasovskii functional; Markov processes; Markovian jump BAM neural networks; Mathematical models; Neural networks; Programming theory; Stability; Theoretical computing; Time delay; Global exponential stability; Impulse control; Leakage delays; Lyapunov–Krasovskii functional; Markovian jump BAM neural networks; Lyapunov method; Continuous time; Stochastic process; Exponential stability; Delay; Bidirectional associative memory; Markov chain; Associative memory; Time varying system; Pulse response; Jump process; Delay time; Integral transformation; Leak; Model driven architecture; Stochastic stability; Delay system; Neural network; Distributed system; regime switching model; Global stabilization; Discrete time; Derivative; Lyapunov-Krasovskii functional; Jumping; Heteroassociation; Lyapunov function
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2014.01.018

This paper deals with the globally exponential stability of impulsive bidirectional associative memory (BAM) neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are determined by a continuous-time, discrete-state Markov chain. Different from the previous literature, the mixed time delays considered here comprise discrete, distributed and leakage time-varying delays. By using the Lyapunov–Krasovskii functional having triple integral terms and model transformation technique, some novel sufficient delay-dependent conditions are derived to ensure the globally exponential stability in the mean square of the suggested system. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the theoretical results.