Robust Stability Against Structured and Unstructured Perturbations: New Results
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The classical Lur'e problem considers the stability of a fixed linear time invariant dynamic system perturbed by sector bounded nonlinear feedback. The small gain theorem on the other hand, considers a fixed linear time invariant dynamic system perturbed by stable functions with bounded H norm in the feedback loop. These results provide a way to account for unstructured perturbations of the fixed linear system. In this paper we are concerned with the same problems when the linear system is also subject to parameter perturbations or uncertainties which are not necessarily small. This motivates us to consider a family of interval plants, i.e. plants with transfer function coefficients varying in prescribed ranges. For such families of systems subject to prescribed ranges of parameter perturbations we obtain precise and non-conservative bounds on the level of unstructured perturbations that can be tolerated. We also develop auxiliary results on passivity and strict positive realness which are of interest in their own right.
