Sliding-mode $H_{\infty }$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov–Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the $H_{\infty }$ performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results.