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

Abstract

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.

Synchronization in Finite Time of Fuzzy Neural Networks with Hybrid Delays and Uncertain Nonlinear Perturbations

“…Since Yang and Yang [1,2] proposed fuzzy cellular neural networks (FCNNs) on the basis of traditional cellular neural networks (CNNs) in 1996, many researchers have performed extensive work on this topic due to their application in image processing and pattern recognition, see [3][4][5][6]. However, in the realization of neural networks, the emergence of time delays is unavoidable due to the limitation of velocity information.…”

Hybrid‐triggered fault detection filter design for networked Takagi–Sugeno fuzzy systems subject to persistent heavy noise disturbance

“…Moreover, nonlinear NCS is a dynamic system, and some faults may occur, which will bring undesirable effect to system performance or even stability. Focusing on these issues, researchers have been seeking effective methods 5‐8 and the references therein. Among them, by introducing a stochastic variable with the Bernoulli distribution, the dissipativity problem for T‐S fuzzy neural networks with probabilistic time‐varying delays is proposed in Reference 6, and the Reference 8 gives fault detection filter design method of nonlinear NCSs under the event‐triggered scheme.…”