Limitations of nonlinear discrete periodic control for robust stabilization

Abstract

This paper presents a performance analysis of nonlinear periodically time varying discrete controllers for the robust stabilization of a linear time invariant discrete plant subject to lp unstructured perturbations. Time invariant controllers are distinguished from periodically time varying controllers. It is shown that nonlinear periodic controllers in general give strictly worse performance than that achievable by nonlinear time invariant controllers, for all p ∈ [1, ∞].