Abstract
A new notion of robust F-stability is introduced, based on the recently introduced notion of F-passivity. Necessary and sufficient conditions for the robust F-stabilization under dynamical structured uncertainties are given, in terms of matrix inequalities. If besides dynamical, also statical uncertainties are included, the given conditions are only sufficient. The conditions are not convex, but for two dual classes of plants, it is shown that the conditions are convex, expressed by linear matrix inequalities (LMIs). An algorithm for controller design is given, and is illustrated by academic examples. It is shown that the uncertainty region where the closed-loop system is stable, obtained by the algorithm, is maximal in respect to literature. It is shown that some of the uncertainties/channels can be completely rejected using the control. If the design algorithm with a transformation is applied to simultaneous robust stabilization and robust ℋ∞ performance, it improves the performance that can be obtained using the method based on inclusion of an extra uncertainty block in the purely robust stabilization scheme.
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