Guaranteed Cost H∞ Controller Synthesis for Switched Systems Defined on Semi-algebraic Sets

A methodology to design guaranteed cost H∞ controllers for a class of switched systems with polynomial vector fields is proposed. To this end, we use sum of squares programming techniques. In addition, instead of the customary Carathéodory solutions, the analysis is performed in the framework of Filippov solutions which subsumes solutions with infinite switching in finite time and sliding modes. Firstly, conditions assuring asymptotic stability of Filippov solutions pertained to a switched system defined on semi-algebraic sets are formulated. Accordingly, we derive a set of sum of squares feasibility tests leading to a stabilizing switching controller. Finally, we propose a scheme to synthesize stabilizing switching controllers with a guaranteed cost H∞ disturbance attenuation performance. The applicability of the proposed methods is elucidated thorough simulation analysis.