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 l_p specific and uniform disturbances. Earlier results on l₂ performance are extended to l₁ and l_∞ performance to present a unified treatment of l_p performance for all p ε 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 l_p disturbance rejection performance than the time varying periodic controller.