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

Wang, Jian Liang; Yang, Guang-Hong; Liu, Jian

Automatica 43, No. 9, 1656-1665 (2007).

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.

MSC:

93B35	Sensitivity (robustness)
93B07	Observability
93C05	Linear systems in control theory

Keywords:

\(\mathcal H_{-}\) index; minimum singular value; minimum sensitivity; fault detection

References:

[1]	Boyd, S. P.; Ghaoui, L. E.; Feron, E.; Balakrishnam, V., Linear matrix inequalities in system and control theory (1994), SIAM: SIAM Philadelphia
[2]	Cao, Y.; Sum, Y.; Lam, J., Simultaneous stabilization via static output feedback and state feedback, IEEE Transactions on Automatic Control, 44, 1277-1282 (1999) · Zbl 0955.93044
[3]	Chen, J.; Patton, R. J., Robust model-based fault diagnosis for dynamic systems (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0920.93001
[4]	Chilali, M.; Gahinet, P.; Apkarian, P., Robust Pole Placement in LMI Regions, IEEE Trans. Automatic Control, 44, 12, 2257-2270 (1999) · Zbl 1136.93352
[7]	Ding, S. X.; Jeinsh, T.; Frank, P. M.; Ding, E. L., A unified approach to the optimization of fault detection systems, International Journal of Adaptive Control and Signal Processing, 14, 7, 725-745 (2000) · Zbl 0983.93016
[8]	Ding, X.; Guo, L.; Jeinsch, T., A characterization of parity space and it’s application to robust fault detection, IEEE Transactions on Automatic Control, 44, 2, 337-343 (1999) · Zbl 0958.93019
[9]	Frank, P., Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey and some new results, Automatica, 26, 3, 459-474 (1990) · Zbl 0713.93052
[10]	Frank, P. M.; Ding, X., Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of Process Control, 7, 6, 403-424 (1997)
[11]	Gertler, J., Survey of model-based failure detection and isolation in complex plants, IEEE Control Systems Magazine, 8, 6, 3-11 (1988)
[13]	Isermann, R., Process fault detection based on modeling and estimation methods: A survey, Automatica, 20, 4, 387-404 (1984) · Zbl 0539.90037
[15]	Liu, J.; Wang, J. L.; Yang, G. H., Reliable guaranteed variance filtering against sensor failures, IEEE Transactions on Signal Processing, 51, 5, 1403-1411 (2003) · Zbl 1369.94210
[17]	Liu, J.; Wang, J. L.; Yang, G. H., An LMI approach to minimum sensitivity analysis with application to fault detection, Automatica, 41, 11, 1995-2004 (2005) · Zbl 1087.93019
[22]	Rank, M. L.; Niemann, H., Norm based design of fault detectors, International Journal of Control, 72, 9, 773-783 (1999) · Zbl 0938.93529
[23]	Wang, H. B.; Wang, J. L.; Lam, J., Robust fault detection observer design: Iterative LMI approaches, Journal of Dynamic Systems, Measurement, and Control, 129, 1, 77-82 (2007)
[24]	Willsky, A. S., A survey of design methods for failure detection in dynamic systems, Automatica, 12, 4, 601-611 (1976) · Zbl 0345.93067
[25]	Zhou, K., Essential of robust control (1998), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ