Dissipativity and passivity analysis for discrete-time T–S fuzzy stochastic neural networks with leakage time-varying delays based on Abel lemma approach

In this paper, the problem of dissipativity and passivity analysis for discrete-time T–S fuzzy stochastic neural networks with leakage time-varying delays is investigated based on Abel lemma approach. In order to obtain less conservative results, Jensen inequality, free-weighting matrix approach and Wirtinger-based inequality have been intensively used in the context of time delay systems. In parallel, the above-mentioned approaches have also been applied to discrete time-delay systems. However, it is well-known that these inequalities may introduce an undesirable conservatism in the dissipativity and passivity conditions in the existing available literature. In this paper, we propose an alternative inequality based on Abel lemma, more precisely on the Abel lemma-based finite sum inequalities. By constructing suitable Lyapunov–Krasovskii functional and using the stochastic analysis technique, strictly (Q,S,R)−γ-dissipativity(Q,S,R)−γ-dissipativity and passivity conditions are derived to the concerned neural networks. The proposed criterion that depends on the upper bounds of the leakage time-varying delay is given in terms of linear matrix inequalities, which can be solved by MATLAB LMI Control Toolbox. Finally, numerical examples are shown to demonstrate the usefulness and effectiveness of the proposed methods.