Hierarchy of LMI conditions for the stability analysis of time-delay systems

Assessing stability of time-delay systems based on the Lyapunov–Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on an a priori design of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design proce...

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Bibliographic Details
Published in:Systems & control letters 2015-07, Vol.81, p.1-7
Main Authors: Seuret, A., Gouaisbaut, F.
Format: Article
Language:English
Subjects:
Automatic
Bessel’s inequality
Engineering Sciences
Jensen’s inequality
Lyapunov–Krasovskii functionals
Stability analysis
Time-delay systems
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Summary:Assessing stability of time-delay systems based on the Lyapunov–Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on an a priori design of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequalities which are asymptotically non conservative and then to design functionals driven by these inequalities. The resulting stability conditions form a hierarchy of LMI which is competitive with the most efficient existing methods (delay-partitioning, discretization and sum of squares), in terms of conservatism and of complexity. Finally, some examples show the efficiency of the method.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2015.03.007