Optimal robust disturbance attenuation for continuous time-varying systems

We consider the optimal robust disturbance attenuation problem (ORDAP) for continuous time-varying systems subject to time-varying unstructured uncertainty. We show that for causal (possibly time-varying) continuous systems, ORDAP is equivalent to finding the smallest fixed point of a “two-disk” type optimization problem under time-varying feedback control laws. Duality is applied in the context of nest algebra of causal stable systems, to prove existence of optimal continuous time-varying controllers. We also show that for time-invariant nominal plants, time-varying control laws offer no improvement over time-invariant feedback control laws and hence generalizing previous results obtained for discrete time-varying systems