L2-Gain Analysis and Control Design of Linear Systems with Input Saturation using Matrix Sum of Squares Relaxation

In this paper, matrix sum of squares (SOS) relaxation is used for analysis of linear systems with input saturation. On the basis of a polytopic type saturation model, we consider a polynomial type saturation model which leads less conservative analysis of Lscr₂ -gain performance. The idea is also applicable to design problems. Both the analysis and the design problems are reduced to robust linear matrix inequality problems that can be solved by using a matrix SOS technique. A structural reduction for the relaxation is also discussed. Finally, numerical examples are shown