Stability and Stabilization of Piecewise Affine and Hybrid Systems: An LMI Approach

In this paper we present various algorithms both for stability analysis and state-feedback design for discrete-time piecewise affine systems. As in [13], our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discrete-time case. Moreover, the basic algorithms are made less conservative by exploiting the switching structure of piecewise affine systems and by using relaxation procedures.