On the robustness analysis of nonlinear systems subject to time-invariant and/or time-varying uncertainty

We propose a novel approach for computing lower bounds on robust stability or performance for nonlinear systems subject to time-invariant and/or time-varying uncertainty. The approach exploits the binary coding mechanism used in defining chromosomes for evolutionary search algorithms, in order to allow the uncertain parameter space to be searched over time, thus allowing the computation of destabilising time-varying uncertain parameters. The resulting lower bounds can be used to check the conservatism of upper bounds computed using tools such as the Popov Criterion, IQC's and various extensions of the structured singular value theory. The usefulness of the proposed approach is illustrated via an example.