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

In this paper we present various algorithms both for stability analysis and state-feedback design for discretetime piecewise aÆne systems. As in [9], 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 discretetime case. Moreover, the basic algorithms are made less conservative by exploiting the switching structure of piecewise aÆne systems and by using relaxation procedures.