Robust Performance for Time-Varying Systems: A functional Analytic Approach

An optimal robust performance problem for discrete time systems, subject to time-varying unstructured uncertainty, is considered in the l² induced norm topology. For a class of nominal plants, an equivalence to an implicit form of a ´two block´ type optimization is established for the case where robustly stabilizing feedback control laws are allowed to be time-varying. The description of this problem in a predual space leads to the conclusion that time-varying control laws offer no improvement over time-invariant feedback from the point of view of optimizing the measure of robust performance considered.