Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity

Abstract

This paper is concerned with on the event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity. Firstly, the principle of the global convergence in fixed time with respect to nonlinear systems with semi-Markov switching is developed. Secondly, in order to realize the global stochastic synchronization goal in fixed time, a novel hybrid controller, which is composed of the event-triggered controller and the switching state-feedback controller, is designed. Under Filippov differential inclusion framework, by applying Lyapunov functional method and inequality analysis technique, the global stochastic synchronization conditions in fixed time are achieved in the form of linear matrix inequalities (LMIs). In addition, the upper bound of the stochastic settling time, which is adjusted in advance by choosing the controller parameters, is estimated accurately. Finally, the correctness of the theoretical results and the feasibility of the designed controller are verified by an example.