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 ∞ performance. Next, an integral sliding surface is designed to guarantee that the

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... op 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.