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An LMI approach to minimum sensitivity analysis with application to fault detection. (English) Zbl 1087.93019
Summary: This paper systematically studies the minimum input sensitivity analysis problem. The lowest level of sensitivity of system outputs to system inputs is defined as an $$\mathcal H$$ index. A full characterization of the $$\mathcal H$$ index is given, first, in terms of matrix equalities and inequalities, and then in terms of linear matrix inequalities (LMIs), as a dual of the Bounded Real Lemma. A related problem of input observability is also studied, with new necessary and sufficient conditions given, which are necessary for a fault detection system to have a nonzero worst-case fault sensitivity. The above results are applied to the problem of fault detection filter analysis, with numerical examples given to show the effectiveness of the proposed approaches.

##### MSC:
 93B35 Sensitivity (robustness) 93B36 $$H^\infty$$-control
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##### References:
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