Robust performance for both fixed and worst case inputs

We consider the problem of robust performance analysis when some of the exogenous inputs acting on the system are assumed to be fixed and known, while others are unknown but bounded. In the special case when all the exogenous inputs are fixed and known, we extend previous results for the unstructured case to the general MIMO case where the perturbation is allowed to be structured. In this case we present both upper and lower bounds for the measure of robust performance. In the more general case, where both fixed and worst case inputs act on the system, we propose a new sufficient condition for robust performance. All these conditions are readily computable, and yield much less conservative results than one would obtain from applying standard worst-case analysis methods.