Abstract
In this paper the issue of strong robustness of sets of systems is introduced and motivated in a scenario of adaptive control. A set of systems is said to be time-invariant strongly robust if the optimal control law designed on the basis of any element in this set stabilizes any other fixed member of the set. A stronger notion amounts to requiring that time-varying stabilizing control laws designed on the basis of any sequence of elements in the set asymptotically or quadratically stabilizes any other fixed member of the set. In this case, the set of systems is said to be time-varying strongly robust or time-varying strongly quadratically robust. The framework is exhibited for a class of linear and time-invariant SISO systems in discrete-time with fixed order n for a specified class of control objectives. It is established that if a given set of systems satisfies some robustness measures involving the classical structured real or complex radius, then the set is strongly robust. Then, for a more specific class of control objectives, attention is paid to the case of polyhedral sets of systems. A characterization of time-varying strongly quadratically robust sets of systems is given in the form of a feasibility test on a finite set of linear matrix inequalities (LMI's).
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