G. Ferrari-Trecate, F. A. Cuzzola, D. Mignone, and M. Morari. Analysis and control with performance of piecewise affine and hybrid systems. Technical Report AUT00-23, Automatic Control Laboratory, ETH Zurich, 2000. http://control.ethz.ch/
In this paper we investigate some analysis and control problems with performancefor discrete-time hybrid systems in thePiece-Wise Affine form. By using arguments from the dissipativitytheory for nonlinear systems, we show that $H_infty$ analysis and synthesis problems can beformulated and solved via Linear Matrix Inequalities that take into account the switchingstructure of the systems. Moreover, such procedures can be generalized in order to solveboth robust control problems and analysis/synthesis with other performance indices likethe Generalized $H_2$ norm.