This work aims at studying the stability of switched linear systems with impulsive disturbances and at designing a state feedback switched control. The conditions are based on Lyapunov-Metzler inequalities, which assure that stability is preserved even if the system evolves on a sliding mode. A slight modification of these inequalities is introduced to cope with a guaranteed cost performance. In order to analyze the quality of the proposed solution, a lower bound for the actual cost is calculated. The theoretical results are applied to a multiobjective H2 control design problem with a number of possibly conflicting criteria. It is shown that the use of switched linear systems theory in multiobjective H2 control problems provides better results than others methods available in the literature. Academic examples are used for illustration.
switched systems; H2 control; continuoustime systems; Lyapunov-Metzler inequalities
