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This paper addresses the problem of robust stability of discrete-time switched systems with time-varying delays and polytopic uncertainties. It is supposed that the switched systems are composed of both stable and unstable subsystems. Delay-dependent sufficient conditions for robust exponential stability are proposed by employing parameter-dependent piecewise Lyapunov-like functional combined with the free-weighting matrix and average dwell time methods. These sufficient conditions are applied in the study of stability analysis for a network-based reliable control system with controller failures, and the effectiveness of the analysis procedure is demonstrated with numerical simulation on network-based reliable control of cart-pendulum.