Abstract
This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞norm of a transfer function to the Riccati matrix inequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.
Similar content being viewed by others
References
Heinen, J. A., Sufficient conditions for stability of interval matrices, International Journal of Control, 1984, 39: 1323.
Argoun, M. B., On sufficient conditions for the stability of interval matrices, International Journal of Control, 1986, 44: 1245.
Zhou, K., Khargonekar, P. P., Stability robustness bounds for state space models with structured uncertainty, IEEE Transaction on Automatic Control, 1987, 32: 621.
Bernstein, D. S., Haddad, W. M., Robust stability and performance analysis for linear dynamic systems, IEEE Transaction on Automatic Control. 1989, 34: 751.
Fang, Y., Loparo, K. A., Feng, X., Sufficient conditions for the stability of interval matrices, International Journal of Control, 1993, 58:969.
Sezer, M. E., Siljak, D. D., On stability of interval matrices, IEEE Transaction on Automatic Control, 1994, 39: 368.
Rern, S., Kabamba, P. T., Bernstein, D. S., Guardian map approach to robust stability of linear systems with constant real parameter uncertainty, IEEE Transaction on Automatic Control, 1994, 39: 162.
Gao, W. B., Motion Stability (in Chinese), Beijing: Higher Education Press, 1987, 135–166.
Boyd, S., Balakrishnan, V., Kabamba, P., A bisection method for computing theH ∞ norm of a transfer matrix and related problems. Math, of Control, Signals and Systems, 1989, 2: 207.
Zhou, K., Khargonekar, P. P., An algebraic Riccati equation approach to H∞ optimization, Systems & Control Letters, 1988. 11: 85.
Author information
Authors and Affiliations
About this article
Cite this article
Zhang, G., Jia, Y. Robust stability of interval parameter matrices. Chin. Sci. Bull. 45, 976–980 (2000). https://doi.org/10.1007/BF02884973
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02884973