In this paper, we consider the use of periodic controllers for simultaneous stabilization and step tracking, including the case when there are occasional, though persistent, plant changes. We consider the case of a finite set of admissible models; we provide a design procedure that yields a controller which stabilizes each such model while providing near optimal LQR step tracking. We then demonstrate that this controller 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.