New qualitative methods for stability of delay systems

Erik I. Verriest

Kybernetika (2001)

  • Volume: 37, Issue: 3, page [229]-238
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Verriest, 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

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