Dissipativity analysis for discrete stochastic neural networks with Markovian delays and partially known transition matrix

Abstract

The problem of dissipativity analysis for a class of discrete-time stochastic neural networks with discrete and finite-distributed delays is considered in this paper. System parameters are described by a discrete-time Markov chain. A discretized Jensen inequality and lower bounds lemma are employed to reduce the number of decision variables and to deal with the involved finite sum quadratic terms in an efficient way. A sufficient condition is derived to ensure that the neural networks under consideration is globally delay-dependent asymptotically stable in the mean square and strictly (Z,S,G)-α-dissipative. Next, the case in which the transition probabilities of the Markovian channels are partially known is discussed. Numerical examples are given to emphasize the merits of reduced conservatism of the developed results.