An LMI approach to stabilization of linear discrete-time periodic systems

Abstract

The problem of stabilization of linear discrete-time periodic systems is considered. LMI based conditions for stabilization via static periodic state feedback as well as via static periodic output feedback are presented. In the case of state feedback, the conditions are necessary and sufficient whereas for output feedback the result is only sufficient as it depends on the particular state-space representation used to describe the system. The problem of quadratic stabilization in the presence of either norm-bounded or polytopic parameter uncertainty is also treated. As an application of the output feedback stabilization technique, we consider the problem of designing a stabilizing (respectively, quadratically stabilizing) static periodic output feedback controller for linear time-invariant discrete-time systems which are not stabilizable (respectively, quadratically stabilizable) by static constant output feedback.