For a state-dependent switching system, when the flow moves across the state boundary, the switching of the subsystem occurs. It is difficult to use a single map to represent the periodic motion with complex mapping structure for such a system without smoothing the system. In this paper, a method is presented to mathematically describe the periodic motion of a piecewise-defined dynamical system using a set of maps. The switchability conditions for a flow on the state boundaries are discussed analytically. The major maps are determined based on the mapping structure of the periodic motion, and the analytical conditions of the flow switchability. The minor maps which correspond to the respective subsystems, are constructed using numerical integration technique. The periodic motions which contain the major maps and minor maps are solved by the Newton-Raphson method. The Jacobian matrix for determining the stability of the periodic motion for such a piecewise-defined system are derived. The Chua’s circuit system which is one of the typical piecewise linear system is used to verify the proposed method by comparing it with the analytic results. Such a hybrid-map representation method can be adopted to investigate the analytical bifurcation and hidden behaviors for a piecewise nonlinear dynamical system.