Robust performance in systems with parametric uncertainty

The problem of checking the infinity norm of a transfer matrix that depends on a number of uncertain bounded parameters for being less than one (or any given bound) over all variations of the parameters is investigated. The problem is shown to be equivalent to checking robust stability with respect to the uncertain parameters in a system that is constructed from the given one by routine state-space calculations. The results allow many important robustness analysis problems to be solved efficiently. In particular, they can be used to check the robust performance of feedback systems with real parametric uncertainty and to check robust stability when that model uncertainty is expressed in terms of unknown but bounded real parameters and unmodeled dynamics lumped in one location in the feedback path. The results completely circumvent the need for manipulations with multivariate polynomials. Robust stability in the equivalent problem can be checked by only one multivariable stability margin computation