G. Ferrari-Trecate, F. A. Cuzzola, D. Mignone, and M. Morari. Analysis of discrete-time piecewise affine and hybrid systems. Technical Report AUT01-16, Automatic Control Laboratory, ETH Zurich, 2001. http://control.ethz.ch/
In this paper we present various algorithms both for stability and performance analysis of discrete-time Piece-Wise Affine (PWA) systems. For stability, different classes of Lyapunov functions are considered and it is shown how to compute them through Linear Matrix Inequalities that take into account the switching structure of the systems. We also show that the continuity of the Lyapunov function is not required in the discrete-time case. Moreover, the tradeoff between the degree of conservativeness and computational requirements is discussed. Finally, by using arguments from the dissipativity theory for nonlinear systems, we generalize our approach to solve $H_infty$ and generalized $H_2$ analysis problems.