Limitations of nonlinear periodic sampled-data control for robust stabilization

Abstract

This paper presents a performance analysis of nonlinear periodically time varying sampled-data controllers acting upon a linear time invariant plant. Time invariant controllers are distinguished from strictly periodically time varying controllers. For a given nonlinear strictly 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 robust stabilization of Lp unstructured perturbations, for all p ∈ [1,∞].