This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is assumed to be constrained. The objective of the proposed controller is to stabilize the switched system under arbitrary switching signals based on the switched Lyapunov function approach. Therefore, based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities. Through online solving an optimization problem, the predictive state-feedback controller is designed. Furthermore, in this delay-dependent approach, only the upper bound of time-delay should be known. Appropriate transient response, ability to handle constraints, and nonconstrained switching signal are the other advantages of the proposed method. Finally, the performance of the proposed approach is compared with a similar approach through a numerical example. As well as, to show the applicability of the proposed controller, it is applied to a drinking water supply network, as an application example.