Robust performance against slowly-varying structured perturbations

Considers the problem of robust performance analysis for some nominal system M(z) against bounded, linear, time-varying, structured feedback perturbations. The authors introduce a natural notion of rate-of-variation for a linear time-varying operator. The authors then exhibit upper and lower bounds on the maximum rate-of-variation of these perturbations against which robust performance is achievable. Using these bounds, it is shown that the existence of frequency dependent D-scales that render the norm of M(z) less than one is necessary and sufficient for robust performance against arbitrarily slowly varying structured linear perturbations of norm less than one. This result suggests that it is natural and well justified to deal with the frequency-dependent upper bound for the μ “norm”, rather than μ itself. This is reassuring given that the upper bound is easily and reliably computable, while computation of complex μ appears difficult