Synthesis of Razumikhin and Lyapunov–Krasovskii approaches to stability analysis of time-delay systems

Synthesis of Razumikhin and Lyapunov–Krasovskii approaches to stability analysis of time-delay systems

In this paper, a necessary and sufficient condition for the exponential stability of linear systems with several time-delays is presented. Such a condition is based on the construction of quadratic lower bounds for the Lyapunov-Krasovskii functionals on the special Razumikhin-type set of functions....

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Veröffentlicht in:Automatica (Oxford) 2015-01, Vol.51, p.372-377
Hauptverfasser: Medvedeva, Irina V., Zhabko, Alexey P.
Format: Artikel
Sprache:eng
Schlagworte:
Automation
Construction
Functionals
Linear systems
Lower bounds
Stability
Stability analysis
Synthesis
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Zusammenfassung:In this paper, a necessary and sufficient condition for the exponential stability of linear systems with several time-delays is presented. Such a condition is based on the construction of quadratic lower bounds for the Lyapunov-Krasovskii functionals on the special Razumikhin-type set of functions. The result reveals a constructive procedure for the stability analysis whose application is illustrated with examples.
ISSN:0005-1098
DOI:10.1016/j.automatica.2014.10.074