An LMI approach to \(\mathcal H_{-}\) index and mixed \(\mathcal H_{-} / \mathcal H_{\infty}\) fault detection observer design. (English) Zbl 1128.93321

Summary: Using the newly developed worst-case fault sensitivity measure, the \(\mathcal H_{-}\) index, and the well-known worst-case robustness measure, the \(\mathcal H_{\infty}\) norm, this paper addresses the problem of \(\mathcal H_{-}\) index fault detection observer design and multiobjective \(\mathcal H_{-}/\mathcal H_{\infty}\) fault detection observer design problems. Necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. Both infinite frequency range case \([0,\infty \)) and finite frequency range case \([0,\overline {\omega})\) are considered. Iterative linear matrix inequality (ILMI) algorithms are given to obtain the solutions. The effectiveness of the proposed approaches is shown by numerical examples.


93B35 Sensitivity (robustness)
93B07 Observability
93C05 Linear systems in control theory
Full Text: DOI


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