Near optimal LQR step tracking for a finite set of LTI plants

In this paper we consider the use of periodic controllers for simultaneous stabilization and step tracking, including the case when there is an occasional, though persistent, plant change. We consider the case of a finite set of admissible models; we provide a design procedure which yields a controller which stabilizes each such model and provides near optimal LQR step tracking, and then demonstrate, via simulation, that it has the facility to tolerate occasional (but persistent) switches between these models without an undue effect on the performance. The controller is periodic with a slight nonlinearity.