Trajectory Tracking for a Class of $\theta$-Periodic Switched Systems.

This paper deals with the trajectory tracking problem of a class of switched systems, whose dynamic matrices are periodic with respect to a parameter $\theta$ that can be a time- or state-dependent function. The design conditions are expressed in terms of linear matrix inequalities and ensure asymptotic tracking of a pre-specified trajectory along with a guaranteed cost of performance. Two three-phase electrical systems are used for motivation and to validate the proposed theory: an ac-dc power converter and a permanent magnet synchronous machine (PMSM). An experimental arrangement has been elaborated to implement the switching strategy in the PMSM and to compare it with other results from the literature.