The main contribution of this paper is to present some controller synthesis results for the discrete-time nonlinear (Lipschitz-like) switching systems. Under the assumption that the discrete state of switching systems is known, three related problems are considered, which are full-state feedback controller design, continuous state observer design, and observer-based output feedback controller design. The basic idea of the proposed approaches is to construct the different types of Hybrid Lyapunov function to guarantee the stability, and all of these methods are given in terms of linear matrix inequalities. The results obtained in this paper are only dependent on the Lipschitz-like constant matrices without regard to the specific nonlinear forms. Finally, a numerical example made up of two subsystems is given to show the applicability of theoretical results.