Performance analysis of periodic control for l1 and l∞ disturbance rejection

This paper presents a performance analysis of discrete time periodically time varying controllers for the rejection of lp specific and uniform disturbances. Earlier results on l2 performance are extended to l1 and l∞ performance to present a unified treatment of lp performance for all pΕ[1,∞]. For a given linear time varying periodic controller, a linear time invariant controller is constructed and necessary and sufficient conditions are presented under which the linear time invariant controller gives strictly better lp disturbance rejection performance than the time varying periodic controller.