G. Ferrari-Trecate, F.A. Cuzzola, and M. Morari. Analysis of piecewise affine systems with logic states. In C. J. Tomlin and M. R. Greenstreet, editors, Proc. 5th International Workshop on Hybrid Systems: Computation and Control , volume 2289 of Lecture Notes in Computer Science , pages 194--208. Springer-Verlag, 2002.
In this paper we consider discrete-time piecewise affine hybridsystems with Boolean inputs, outputs and states and we show thatthey can be represented in a 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 $H_infty$analysis problem.