Analysis of discrete-time piecewise affine and hybrid systems

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 discrete time. 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 analyze the l₂-gain of PWA systems.