Stabilization of linear discrete-time periodic systems with uncertain period

In this paper, stabilization problem for constrained linear discrete-time periodic systems with uncertain period is investigated, where the uncertain period is caused by the probabilistic transitions of some mode to the next mode or to itself. Results are given for three cases, robust stabilization, stochastic stabilization by utilizing the transition probabilities, and MPC design. All these designs are based on the use of mode-dependent state feedback control law. Conditions guaranteeing the close-loop stability and satisfaction of constraints on inputs and states are given in terms of LMIs. Finally a numerical example is given to verify the efficiency of the developed results.