Limitations of nonlinear discrete periodic control for disturbance attenuation and robust stabilization

This paper presents a performance analysis of nonlinear periodically time-varying discrete controllers acting upon a linear time-invariant discrete plant. Time-invariant controllers are distinguished from strictly periodically time-varying controllers. For a given nonlinear periodic controller, a time-invariant controller is constructed. Necessary and sufficient conditions are given under which the time-invariant controller gives strictly better control performance than the time-invariant controller from which it was obtained, for the attenuation of l_p exogenous disturbances and the robust stabilization of l_p unstructured perturbations, for all p[1,∞].