Stabilization of Discrete-Time Piecewise Affine Systems in Implicit Representation

This paper addresses the problem of stabilization of discrete-time piecewise affine (PWA) systems. The design of a piecewise affine state feedback control law is studied using an implicit representation based on ramp functions. LMI-based stability conditions, obtained from a piecewise quadratic Lyapunov function and the implicit representation, are stated to assess the global exponential stability of the origin of the closed-loop PWA system. Through appropriate congruence transformations and some structural assumptions, a method to design the control law parameters using semidefinite programming is then proposed.