Dissipativity analysis for discrete time-delay fuzzy neural networks with Markovian jumps

Abstract

This paper is concerned with the dissipativity analysis and design of discrete Markovian jumping neural networks with sector-bounded nonlinear activation functions and time-varying delays represented by Takagi–Sugeno fuzzy model. The augmented fuzzy neural networks with Markovian jumps are first constructed based on estimator of Luenberger observer type. Then, applying piecewise Lyapunov–Krasovskii functional approach and stochastic analysis technique, a sufficient condition is provided to guarantee that the augmented fuzzy jump neural networks are stochastically dissipative. Moreover, a less conservative criterion is established to solve the dissipative state estimation problem by using matrix decomposition approach. Furthermore, to reduce the computational complexity of the algorithm, a dissipative estimator is designed to ensure stochastic dissipativity of the error fuzzy jump neural networks. As a special case, we have also considered the mixed H∞ and passive analysis of fuzzy jump neural networks. All criteria can be formulated in terms of linear matrix inequalities. Finally, two examples are given to show the effectiveness and potential of the new design techniques.