G. Ferrari-Trecate, F.A. Cuzzola, and M. Morari. Lagrange stability and performance analysis of discrete-time piecewise affine systems with logic states. International Journal of Control , 76(16):1585--1598, 2003.
In this paper we consider discrete-time piecewise affine hybridsystems with boolean inputs, outputs and states and show that theycan be represented in a logic canonical form where the logicvariables influence the switching between different submodels butnot the continuous-valued dynamics. We exploit this representationfor studying Lagrange stability and developing performanceanalysis procedures based on linear matrix inequalities. Moreover,by using arguments from dissipativity theory for nonlinearsystems, we generalize our approach to solve the H-infinityanalysis problem.