×
Qiu, L.; Davison, E. J.

Feedback stability under simultaneous gap metric uncertainties in plant and controller. (English) Zbl 0743.93083

Syst. Control Lett. 18, No. 1, 9-22 (1992).
Summary: The stability robustness of a feedback system is studied by assuming that the plant and the controller are subject to independent uncertainties and that the uncertainties are measured by the gap metric. A fairly complete solution is obtained by exploring the trigonometric structure of the graphs of the plant and the controller.

Cited in 24 Documents

MSC:

93D15 Stabilization of systems by feedback
93D09 Robust stability

Keywords:

stability robustness
Cite Review PDF
Full Text: DOI

References:

[1] Björck, Å.; Golub, G. H., Numerical method for computing angles between linear subspaces, Math. Comput., 27, 579-593 (1973) · Zbl 0282.65031
[2] Davis, C.; Kahan, W. M., The rotation of eigenvectors by a perturbation III, SIAM J. Numer. Anal., 7, 1-46 (1970) · Zbl 0198.47201
[3] Englehart, M. J.; Smith, M. C., A four-block problem for \(H_∞\) design: properties and applications, (Proc. IEEE CDC (1990)), 2401-2406 · Zbl 0765.90001
[4] Foias, C.; Georgiou, T. T.; Smith, M. C., Geometric techniques for robust stabilization of linear time-varying systems, (Proc. IEEE CDC (1990)), 2868-2873
[5] Francis, B. A., A Course in \(H_∞\) Control Theory (1986), Springer-Verlag: Springer-Verlag New York
[6] Georgiou, T. T., On the computation of the gap metric, Systems Control Lett., 11, 253-257 (1988) · Zbl 0669.93039
[7] Georgiou, T. T.; Smith, M. C., Optimal robustness in the gap metric, IEEE Trans. Automat. Control, 35, 673-685 (1990) · Zbl 0726.93059
[8] Glover, K.; McFarlane, D.c., Robust stabilization of normalized coprime factor plant description with \(H_∞\)-bounded uncertainty, IEEE Trans. Automat. Control, 34, 821-830 (1989) · Zbl 0698.93063
[9] Gohberg, I.; Lancaster, P.; Rodman, L., Invariant Subspaces of Matrices with Applications (1986), Wiley: Wiley New York · Zbl 0608.15004
[10] Halmos, P. R., A Hilbert Space Problem Book (1982), Springer-Verlag: Springer-Verlag New York · Zbl 0144.38704
[11] Kato, T., Perturbation Theory for Linear Operator (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0148.12601
[12] Qui, L.; Davison, E. J., Pointwise gap metric on transfer matrices, (Proc. IEEE CDC. Proc. IEEE CDC, IEEE Trans. Automat. Control (1990)), 2431-2436, to appear in
[13] Vidyasagar, M., The graph metric for unstable plants and robustness estimates for feedback stability, IEEE Trans. Automat. Control.sbst, 29, 403-418 (1984) · Zbl 0536.93042
[14] Vidyasagar, M., Control System Synthesis: A Factorization Approach (1985), MIT Press: MIT Press Cambridge, MA · Zbl 0655.93001
[15] Vidyasagar, M.; Kimura, H., Robust controllers for uncertain linear multivariable systems, Automatica, 22, 85-94 (1986) · Zbl 0626.93057
[16] Zames, G.; El-Sakkary, A. K., Unstable systems and feedback: the gap metric, (Proc. 16th Allerton Conf. (1980)), 380-385
[17] Zhu, S. Q., Graph topology and gap topology for unstable systems, IEEE Trans. Automat. Control, 34, 848-855 (1989) · Zbl 0697.93030
[18] Zhu, S. Q.; Hautus, M. L.J.; Praagman, C., Sufficient conditions for robust BIBO stabilization: given by the gap metric, Systems Control Lett., 11, 53-59 (1988) · Zbl 0651.93056
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.