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On the small-$$\mu$$ theorem. (English) Zbl 0831.93021
Summary: Counterexamples to a commonly quoted statement of the small-$$\mu$$ theorem are exhibited. We exhibit plants $$P$$ with unit ‘$$\mu$$-norm’ that cannot be destabilized by any real-rational stable proper structured uncertainty of size one. A detailed proof of a correct statement is provided. It includes the case where the uncertainty is not constrained to be real- rational.

##### MSC:
 93B35 Sensitivity (robustness) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93B36 $$H^\infty$$-control
##### Software:
Mu Analysis and Synthesis Toolbox
Full Text:
##### References:
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