G. Ferrari-Trecate, F.A. Cuzzola, D. Mignone, and M. Morari. Analysis of discrete-time piecewise affine and hybrid systems. Automatica , 38:2139--2146, 2002.
In this paper we present various algorithms both for stability andperformance analysis of discrete-time Piece-Wise Affine (PWA)systems. For stability, different classes of Lyapunov functionsare considered and it is shown how to compute them through LinearMatrix Inequalities that take into account the switching structureof the systems. We also show that the continuity of the Lyapunovfunction is not required in the discrete-time case. Moreover, thetradeoff between the degree of conservativeness and computationalrequirements is discussed. Finally, by using arguments from thedissipativity theory for nonlinear systems, we generalize ourapproach to analyze the $l_2$-gain of PWA systems.