×

A new discrete-time robust stability condition. (English) Zbl 0948.93058

Summary: A new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given. It enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. It is shown that this new condition provides better results than the classical quadratic stability. Besides the use of a parameter-dependent Lyapunov function, this condition exhibits a kind of decoupling between the Lyapunov and the system matrices which may be explored for control synthesis purposes. A numerical example illustrates the results.

MSC:

93D30 Lyapunov and storage functions
93D09 Robust stability
93C55 Discrete-time control/observation systems
15A39 Linear inequalities of matrices
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barmish, B. R., A generalization of kharitonov four-polynomial concept for robust stability problems with linearly dependent coefficient perturbations, J. Optim. Theory Appl., 46, 399-408 (1985) · Zbl 0549.93045
[2] S.P. Battacharyya, H. Chapellat, L.H. Keel, Robust Control: the Parametric Approach, Prentice-Hall, Upper Saddle River, NJ, 1997.; S.P. Battacharyya, H. Chapellat, L.H. Keel, Robust Control: the Parametric Approach, Prentice-Hall, Upper Saddle River, NJ, 1997.
[3] Bernussou, J.; Geromel, J. C.; Peres, P. L.D., A linear programming oriented procedure for quadratic stabilization of uncertain systems, Systems Control Lett., 13, 1, 65-72 (1989) · Zbl 0678.93042
[4] P. Colaneri, J.C. Geromel, A. Locatelli, Control Theory and Design: An \(RH_2 RH_∞\); P. Colaneri, J.C. Geromel, A. Locatelli, Control Theory and Design: An \(RH_2 RH_∞\)
[5] Fans, M. K.H.; Tits, A. L.; Doyle, J. C., Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics, IEEE Trans. Automat. Control, 36, 1, 25-38 (1991) · Zbl 0722.93055
[6] Feron, E.; Apkarian, P.; Gahinet, P., Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions, IEEE Trans. Automat. Control, 41, 7, 1041-1046 (1996) · Zbl 0857.93088
[7] Gahinet, P.; Apkarian, P.; Chilaly, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Trans. Automat. Control, 41, 3, 436-442 (1996) · Zbl 0854.93113
[8] Garofalo, F.; Celentano, G.; Glielmo, L., Stability robustness of interval matrices via Lyapunov quadratic forms, IEEE Trans. Automat. Control, 38, 2, 281-284 (1993) · Zbl 0774.93061
[9] Haddad, W. M.; Kapila, V., Robust stabilization for discrete-time systems with slowly time-varying uncertainty, J. Franklin Inst. — Eng. Appl. Math., 333 B, 1, 71-84 (1996) · Zbl 0849.93053
[10] M.C. de Oliveira, J.C. Geromel, L. Hsu, LMI characterization of structural and robust stability: the discrete-time case, Linear Alg. Appl., to appear.; M.C. de Oliveira, J.C. Geromel, L. Hsu, LMI characterization of structural and robust stability: the discrete-time case, Linear Alg. Appl., to appear. · Zbl 0949.93063
[11] K. Zhou, J.C. Doyle, K. Glover, Robust and Optimal Control, Prentice-Hall, Upper Saddle River, NJ, 1996.; K. Zhou, J.C. Doyle, K. Glover, Robust and Optimal Control, Prentice-Hall, Upper Saddle River, NJ, 1996. · Zbl 0999.49500
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.