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This paper is concerned with the problem of robust stabilization for uncertain switched non-linear systems subject to actuator saturation and time-varying norm-bounded parameter uncertainties. Centred on the problem, a survey on both continuous and discrete-time domains has been made. The non-linearities in the state equations meet with the global Lipschitz conditions. In this paper, we are trying to work out a design of state feedback controllers and a state-dependent switching law so as to make the resulting closed-loop system robustly asymptotically stable at the origin with a large domain of attraction. Using the multiple Lyapunov functions method, some sufficient conditions for robust stabilization are derived. Furthermore, a group of static feedback controllers and a state-dependent switching law are designed, respectively, with an estimation of domain of attraction by solving a optimization problem, which are based on the solutions of certain linear matrix inequalities. Finally, a simulation example is presented to illustrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]