State estimation of T–S fuzzy Markovian generalized neural networks with reaction–diffusion terms: a time-varying nonfragile proportional retarded sampled-data control scheme

Abstract

This paper focuses on the state estimation issue of T–S fuzzy Markovian generalized neural networks (GNNs) with reaction–diffusion terms. An estimator-based nonfragile time-varying proportional retarded sampled-data controller that permits norm-bounded indeterminacy and contains a time-varying delay is designed to guarantee the asymptotical stability of the error system. By establishing a novel Lyapunov–Krasovskii functional that involves positive indefinite items and discontinuous items, meanwhile, by combining the reciprocally convex combination method, Jenson’s inequality and Wirtinger inequality, a less conservative stability criterion can be derived. Moreover, the principle for the number of selected variables in the process of deriving main results is also analyzed. Finally, two numerical examples are given to demonstrate the validity and advantages of the results proposed in this paper.