Robust performance for fixed inputs

We address the problem of robust performance analysis when the exogenous input is assumed to be fixed and known. This differs from standard approaches in the literature which assume that the exogenous input is an unknown element in a class of norm bounded signals. When the performance is measured by the ℓ_∞ norm, and the nominal plant is perturbed by LTV perturbations of bounded ℓ_∞ induced norm, we propose upper and lower bounds for the measure of robust performance. Two upper bounds are derived. The first one can have direct application in robust performance synthesis problems. The second one provides a tighter bound. Both conditions are (usually) much less conservative than the condition resulting from assuming a worst case exogenous input. The necessary condition follows from the result of Khammash for robust steady state performance. For certain classes of input signals, these upper and the lower bounds coincide, providing a necessary and sufficient condition.