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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 thedoi:10.1186/s13662-019-1987-6 fatcat:4v55ohkz3rcutlhxt2k3q65tjm