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 particular, we consider the case where performance is measured by the ℓ_∞ norm of the output signals, and the uncertainty on the nominal model is described by LTV perturbations of bounded ℓ_∞ induced norm. We first address the special case when all the exogenous inputs are fixed and known. We propose upper and lower bounds for the measure of robust performance. Two upper bounds are derived, which trade off accuracy versus computational expense. Both conditions are much less conservative than what one would obtain from assuming a worst-case exogenous input. We then generalize the conditions to the more general case, where both fixed and worst-case inputs act on the system. All these conditions are readily computable, and yield much less conservative results than one would obtain from applying standard worst-case analysis methods.