Robustness under Bounded Uncertainty with Phase Information
Robustness under Bounded Uncertainty with Phase Information
A. L. Tits, V. Balakrishnan and L. Lee
IEEE Trans. Aut. Contr., vol. 44, no. 1, pages 50-65, January 1999
Abstract:
We consider uncertain linear systems where the
uncertainties, in addition to being bounded, also satisfy
constraints on their phase. In this context, we define the
``phase-sensitive structured singular value'' (PS-SSV) of a
matrix, and show that sufficient (and sometimes necessary)
conditions for stability of such uncertain linear systems
can be rewritten as conditions involving PS-SSV. We then
derive upper bounds for PS-SSV, computable via convex
optimization. We extend these results to the
case where the uncertainties are structured (diagonal or
block-diagonal, for instance).
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