Dissipativity and passivity analysis of T-S fuzzy neural networks with probabilistic time-varying delays: a quadratic convex combination approach

This paper studied dissipativity and passivity analysis of T-S fuzzy neural networks with distributed and probabilistic time-varying delay via quadratic convex combination approach. By introducing a stochastic variable with the Bernoulli distribution, the fuzzy neural networks with random time delays are transformed into one with deterministic delays and stochastic parameters. Moreover, it is well known that the dissipativity behavior of fuzzy neural networks is very sensitive to the time delay in the leakage term. By constructing proper Lyapunov-Krasovskii functional, new delay-dependent dissipativity and passivity conditions are derived in terms of linear matrix inequalities. Different from previous results, involving the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function. Finally, numerical examples are provided to verify the effectiveness of the presented results.