Stochastic dissipativity and passivity analysis for discrete-time neural networks with probabilistic time-varying delays in the leakage term

This paper deals with the dissipativity and passivity analysis for discrete-time stochastic neural networks with probabilistic time-varying delays. The main contribution of this paper is to reduce the conservatism of the dissipativity conditions for the considered neural networks by utilizing the reciprocally convex combination approach. This approach is proposed to bound the forward differences of the double and triple summable terms taken in the Lyapunov functional. By introducing a stochastic variable with a Bernoulli distribution, the information of probability distribution of the time-varying delays are considered and transformed into one with deterministic time-varying delays. By employing Lyapunov functional approach, sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the considered neural networks to be strictly (Q,S,R)-γ(Q,S,R)-γ-dissipative and passive. Finally, numerical examples are given to demonstrate the effectiveness of the obtained results.