Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control.

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.