Asynchronous boundary stabilization for T-S fuzzy Markov jump delay reaction-diffusion neural networks

Abstract

This paper deals with the exponential boundary stabilization for a class of Markov jump reaction-diffusion neural networks (MJRDNNs) with mixed time-varying delays, which is described by T-S fuzzy model. It is assumed that observed modes in boundary controller are not synchronized with the system modes. Based on a hidden Markov model (HMM), a novel asynchronous boundary control law is developed by using observed modes. Compared with the existing control strategies for distributed parameter systems, the asynchronous boundary control scheme can not only save the cost of the controller installation, but also bring less conservativeness. A delay-dependent sufficient condition to guarantee the exponentially mean square stability is established for T-S fuzzy MJRDNNs with mixed time-varying delays by constructing a Lyapunov functional and utilizing the vector-value Wirtinger-type inequality. Meanwhile, in order to get the designing scheme of the boundary controller, an equivalent LMI-based sufficient criterion is established. In the end, the effectiveness of the proposed results is illustrated by simulation examples.