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

The problem of stabilization of linear discrete-time periodic systems is co nsidered. LMI based conditions for stabilization via static periodic state feedback as well as via static periodic output feedback are presented. In t he case of state feedback, the conditions are necessary and sufficient wher eas for output feedback the result is only sufficient as it depends on the particular state-space representation used to describe the system. The prob lem of quadratic stabilization in the presence of either norm-bounded or po lytopic parameter uncertainty is also treated. As an application of the out put feedback stabilization technique, we consider the problem of designing a stabilizing (respectively, quadratically stabilizing) static periodic out put feedback controller for linear time-invariant discrete-time systems whi ch are not stabilizable (respectively, quadratically stabilizable) by stati c constant output feedback.