Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied.Based on a suitable time-invariant state sampled reformulation,periodic state feedback controller has been designed such that desired require-ments of steady state covariance,H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously.By using satisfactory control theory,the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities(LMIs),and a feasible designing approach is presented via LMI technique.Numeric example validates the obtained conclusion.