$H∞$ Control for Continuous-Time Switched Linear Systems

This paper deals with the output feedback $H∞$ control design problem for continuous-time switched linear systems. More specifically, the main goal is to design a switching rule together with a dynamic full order linear controller to satisfy a prespecified $H∞$ level defined by the $L2$ gain from the input to the output signal. Initially, the state feedback version of this problem is solved in order to put in evidence the main difficulties we have to face toward the solution of the output feedback control design problem. The results reported in this paper are based on the so called Lyapunov–Metzler inequalities, which express a sufficient condition for switched linear systems global stability. The solution of the previously mentioned output feedback control design problem through a linear matrix inequality based method is the main contribution of the present paper. An academic example borrowed from literature is used for illustration.