New qualitative methods for stability of delay systems
Kybernetika (2001)
- Volume: 37, Issue: 3, page [229]-238
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topVerriest, Erik I.. "New qualitative methods for stability of delay systems." Kybernetika 37.3 (2001): [229]-238. <http://eudml.org/doc/33531>.
@article{Verriest2001,
abstract = {A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known qualitative behavior. It leads to criteria for stability of general difference and delay differential equations.},
author = {Verriest, Erik I.},
journal = {Kybernetika},
keywords = {stability of systems; delay system; Lyapunov method; stability of systems; delay system; Lyapunov method},
language = {eng},
number = {3},
pages = {[229]-238},
publisher = {Institute of Information Theory and Automation AS CR},
title = {New qualitative methods for stability of delay systems},
url = {http://eudml.org/doc/33531},
volume = {37},
year = {2001},
}
TY - JOUR
AU - Verriest, Erik I.
TI - New qualitative methods for stability of delay systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 3
SP - [229]
EP - 238
AB - A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known qualitative behavior. It leads to criteria for stability of general difference and delay differential equations.
LA - eng
KW - stability of systems; delay system; Lyapunov method; stability of systems; delay system; Lyapunov method
UR - http://eudml.org/doc/33531
ER -
References
top- Borne P., Dambrine M., Perruquetti, W., Richard J. P., Vector Lyapunov functions for nonlinear time-varying, ordinary and functional differential equations, In: Stability at the End of the XXth Century (Martynyuk, ed.), Gordon and Breach. To appear MR1974827
- Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V., Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia 1994 Zbl0816.93004MR1284712
- Dambrine M., Richard J. P., Stability and stability domains analysis for nonlinear differential-difference equations, Dynamic Systems and Applications 3 (1994), 369–378 (1994) Zbl0807.34089MR1289810
- Dugard L., Verriest E. I., Stability and Control of Time-Delay Systems, Springer–Verlag, London 1998 Zbl0901.00019MR1482570
- Erbe L. H., Kong,, Qingkai, Zhang B. G., Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York 1995 Zbl0821.34067MR1309905
- Hale J. K., Effects of Delays on Stability and Control, Report CDNS97-270, Georgia Institute of Technology
- Hale J. K., Lunel S. M. Verduyn, Introduction to Functional Differential Equations, Springer–Verlag, New York 1993 MR1243878
- Ivanescu D., Dion J.-M., Dugard, L., Niculescu S.-I., Delay effects and dynamical compensation for time-delay systems, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 1999–2004 (1999)
- Laksmikantham V., Leela S., Differential and Integral Inequalities, Vol. I and II. Academic Press, New York 1969
- Laktionov A. A., Zhabko A. P., Method of difference transformations for differential systems with linear time-delay, In: Proc. IFAC Workshop on Linear Time Delay Systems, Grenoble 1998, pp. 201–205 (1998)
- Logemann H., Townley S., 10.1016/0167-6911(96)00002-3, Systems Control Lett. 27 (1996), 267–274 (1996) Zbl0866.93089MR1391712DOI10.1016/0167-6911(96)00002-3
- Michel A. N., Miller R. K., Qualitative Analysis of Large Scale Dynamical Systems, Academic Press, New York 1977 Zbl0494.93002MR0444204
- Perruquetti W., Richard J. P., Borne P., Estimation of nonlinear time-varying behaviours using vector norms, Systems Anal. Modelling Simulation 11 (1993), 167–184 (1993)
- Verriest E. I., Robust stability, adjoints, and LQ control of scale-delay systems, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 209–214 (1999)
- Verriest E. I., Ivanov A. F., Robust stabilization of systems with delayed feedback, In: Proc. 2nd International Symposium on Implicit and Robust Systems, Warsaw 1991, pp. 190–193 (1991)
- Verriest E. I., Ivanov A. F., Robust stability of systems with delayed feedback, Circuits Systems Signal Process. 13 (1994), 2/3, 213–222 (1994) Zbl0801.93053MR1259591
- Xie L., Souza C. E. de, Robust stabilization and disturbance attenuation for uncertain delay systems, In: Proc. 2nd European Control Conference, Groningen 1993, pp. 667–672 (1993)
- Zhabko A. P., Laktionov A. A., Zubov V. I., Robust stability of differential-difference systems with linear time-delay, In: Proc. IFAC Symposium on Robust Control Design, Budapest 1997, pp. 97–101 (1997)
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.