×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Boyd, S. P.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[2] Cevik, M. K.K.; Göknar, I. C., Unknown input observability of decomposed systems consisting of algebraic and integration parts, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 43, 6, 469-472 (1996)
[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] Chen, J.; Patton, R. J.; Liu, G. P., Optimal residual design for fault-diagnosis using multiobjective optimization and genetic algorithms, International Journal of Systems Science, 27, 6, 567-576 (1996) · Zbl 0854.93134
[5] 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
[6] Hou, M.; Muller, P. C., Design of observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 37, 6, 871-875 (1992) · Zbl 0775.93021
[7] Hou, M., & Patton, R. J. (1996). An LMI approach to \(\mathcal{H}_- / \mathcal{H}_\infty\) fault detection observers. In Proceedings of the UKACC international conference on control (pp. 305-310).; Hou, M., & Patton, R. J. (1996). An LMI approach to \(\mathcal{H}_- / \mathcal{H}_\infty\) fault detection observers. In Proceedings of the UKACC international conference on control (pp. 305-310).
[8] Hou, M.; Patton, R. J., Input observability and input reconstruction, Automatica, 34, 6, 789-794 (1998) · Zbl 0959.93006
[9] Liu, J., Wang, J. L., & Yang, G. H. (2002). Worst-case fault detection observer design: an LMI approach. In Proceedings of the international conference on control and automation, Xiamen, China (pp. 1243-1247).; Liu, J., Wang, J. L., & Yang, G. H. (2002). Worst-case fault detection observer design: an LMI approach. In Proceedings of the international conference on control and automation, Xiamen, China (pp. 1243-1247).
[10] 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
[11] Liu, J., Wang, J. L., & Yang G. H. (2003b). An LMI approach to worst case analysis for fault detection observers. In Proceedings of American control conference, Denver, Colorado, USA (pp. 2985-2990).; Liu, J., Wang, J. L., & Yang G. H. (2003b). An LMI approach to worst case analysis for fault detection observers. In Proceedings of American control conference, Denver, Colorado, USA (pp. 2985-2990).
[12] Liu, J., Wang, J. L., & Yang, G. H. (2005). An LMI approach to \(\mathcal{H}_-/ \mathcal{H}_\infty\) fault detection observer design. Automatica, accepted for publication.; Liu, J., Wang, J. L., & Yang, G. H. (2005). An LMI approach to \(\mathcal{H}_-/ \mathcal{H}_\infty\) fault detection observer design. Automatica, accepted for publication.
[13] Nobrega, E. G., Abdalla, M. O., & Grigoriadis, K. M. (2000). LMI-based filter design for fault detection and isolation. In Proceedings of the 39th conference on decision control, Sydney, Australia (pp. 4329-4334).; Nobrega, E. G., Abdalla, M. O., & Grigoriadis, K. M. (2000). LMI-based filter design for fault detection and isolation. In Proceedings of the 39th conference on decision control, Sydney, Australia (pp. 4329-4334).
[14] Park, Y.; Stein, J. L., Closed-loop, state and input observer for systems with unknown inputs, International Journal of Control, 48, 3, 1121-1136 (1988) · Zbl 0659.93007
[15] Patton, R. J., & Hou, M. (1997). \( \mathcal{H}_\infty\) estimation and robust fault detection, In Proceedings of the European control conference, Brussels, Belgium.; Patton, R. J., & Hou, M. (1997). \( \mathcal{H}_\infty\) estimation and robust fault detection, In Proceedings of the European control conference, Brussels, Belgium.
[16] Rambeaux, F., Hamelin, F., & Sauter, D. (1999). Robust residual generation via LMI. In Proceedings of the 14th World Congress of IFAC, Beijing, China (pp. 240-246).; Rambeaux, F., Hamelin, F., & Sauter, D. (1999). Robust residual generation via LMI. In Proceedings of the 14th World Congress of IFAC, Beijing, China (pp. 240-246).
[17] Rank, M. L.; Niemann, H., Norm based design of fault detectors, International Journal of Control, 72, 9, 773-783 (1999) · Zbl 0938.93529
[18] Scherer, C.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, 42, 7, 896-911 (1997) · Zbl 0883.93024
[19] Zhou, K., Essential of robust control (1998), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[20] Zhou, K.; Doyle, J.; Comstock, J., Robust and optimal control (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.