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This paper investigates the stabilisation problem for a class of linear uncertain networked control systems (NCSs) with random communication time-delays. Both sensor-to-controller and controller-to-actuator random network-induced delays are considered. Markov processes are used to model these random network-induced delays. Based on the Lyapunov-Razumikhin method a mode-dependent state feedback controller is proposed to stabilize this class of systems. The existence of such controller is given in terms of the solvability of bilinear matrix inequalities (BMIs), which are to be solved by a newly proposed algorithm. A numerical example is used to illustrate the validity of the design methodology.