Analysis and control with performance of piecewise affine and hybrid systems

In this paper we investigate some analysis and control problems with performance for discrete-time hybrid systems in the Piece-Wise Affine form. By using arguments from the dissipativity theory for nonlinear systems, we show that H ∞ analysis and synthesis problems can be formulated and solved via Linear Matrix Inequalities that take into account the switching structure of the systems. Moreover, such pro-cedures can be generalized in order to solve both robust control problems and anal-ysis/synthesis with other performance indices like the Generalized H2 norm