Constrained state feedback control of piecewise affine systems

This paper deals with constrained state feedback control of piecewise affine systems, an important class of hybrid systems. Our objective is to design stabilizing feedback gains that guarantees, for any arbitrary switching rule, the respect of the control and state constraints. The existence of a solution is first expressed geometrically, in terms of two polyhedral sets inclusion. The geometric conditions is then reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem.