Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems (LPSs) with interval-type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respectively, are given. Problems of L(2)-gain analysis and control synthesis are studied. For the L(2)-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L(2)-gain smaller than a positive scalar gamma. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L(2)-gain smaller than the positive scalar gamma. All the conditions are necessary and sufficient.