Previous |  Up |  Next


Title: New qualitative methods for stability of delay systems (English)
Author: Verriest, Erik I.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 37
Issue: 3
Year: 2001
Pages: [229]-238
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: stability of systems
Keyword: delay system
Keyword: Lyapunov method
MSC: 34K20
MSC: 93C23
MSC: 93D05
MSC: 93D30
idZBL: Zbl 1265.93191
idMR: MR1859082
Date available: 2009-09-24T19:39:02Z
Last updated: 2015-03-26
Stable URL:
Reference: [1] 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 MR 1974827
Reference: [2] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory.SIAM Studies in Applied Mathematics, Philadelphia 1994 Zbl 0816.93004, MR 1284712
Reference: [3] Dambrine M., Richard J. P.: Stability and stability domains analysis for nonlinear differential-difference equations.Dynamic Systems and Applications 3 (1994), 369–378 Zbl 0807.34089, MR 1289810
Reference: [4] Dugard L., Verriest E. I.: Stability and Control of Time-Delay Systems.Springer–Verlag, London 1998 Zbl 0901.00019, MR 1482570
Reference: [5] Erbe L. H., Kong,, Qingkai, Zhang B. G.: Oscillation Theory for Functional Differential Equations.Marcel Dekker, New York 1995 Zbl 0821.34067, MR 1309905
Reference: [6] Hale J. K.: Effects of Delays on Stability and Control.Report CDNS97-270, Georgia Institute of Technology
Reference: [7] Hale J. K., Lunel S. M. Verduyn: Introduction to Functional Differential Equations.Springer–Verlag, New York 1993 MR 1243878
Reference: [8] 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
Reference: [9] Laksmikantham V., Leela S.: Differential and Integral Inequalities.Vol. I and II. Academic Press, New York 1969
Reference: [10] 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
Reference: [11] Logemann H., Townley S.: The effect of small delays in the feedback loop on the stability of neutral systems.Systems Control Lett. 27 (1996), 267–274 Zbl 0866.93089, MR 1391712, 10.1016/0167-6911(96)00002-3
Reference: [12] Michel A. N., Miller R. K.: Qualitative Analysis of Large Scale Dynamical Systems.Academic Press, New York 1977 Zbl 0494.93002, MR 0444204
Reference: [13] Perruquetti W., Richard J. P., Borne P.: Estimation of nonlinear time-varying behaviours using vector norms.Systems Anal. Modelling Simulation 11 (1993), 167–184
Reference: [14] 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
Reference: [15] 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
Reference: [16] Verriest E. I., Ivanov A. F.: Robust stability of systems with delayed feedback.Circuits Systems Signal Process. 13 (1994), 2/3, 213–222 Zbl 0801.93053, MR 1259591
Reference: [17] 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
Reference: [18] 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


Files Size Format View
Kybernetika_37-2001-3_2.pdf 1.313Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo