Fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology

This paper investigates the problem of fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology. The main purpose is to design a fault-tolerant controller so as to make the resultant closed-loop system is stochastically synchronous in the presence of actuator failures. Some sufficient conditions to ensure the presence of the controller are obtained by constructing a mode-dependent Lyapunov-Krasovskii functional and employing some novel inequalities. Based on these conditions, a clear expression for the desired controller is given by using a simple matrix decoupling method. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.