D. Mignone, G. Ferrari-Trecate, and M. Morari. Stability and stabilization of piecewise affine and hybrid systems: An LMI approach. Proc. 39th Conference on Decision and Control , 1, 2000. Sidney, Australia, 12-15 December.
In this paper we present various algorithms both for stability analysis andstate-feedback design for discrete-time piecewise affine systems. As in (Johansson and Rantzer, 1998), ourapproach hinges on the use of piecewise quadratic Lyapunov functions that can be computedas the solution of a set of linear matrix inequalities. We show that the continuity of theLyapunov function is not required in the discrete-time case. Moreover, the basic algorithmsare made less conservative by exploiting the switching structure of piecewise affinesystems and by using relaxation procedures.