H2 control design of Lur’e type switched systems∗

This paper deals with H2 control design of Lur’e-type switched systems through a generalization of the Popov criterion. More specifically, a state-input dependent switching rule is proposed in order to assure global asymptotic stability and H2 guaranteed cost. This new switching strategy is the key point to generalize the celebrated Popov criterion. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed in terms of a certain convex combination of the subsystems state space matrices. Moreover, this test takes into account an H2 performance index whose study in the present context is novel in the literature. The theory is illustrated by an academic example.