Equivalence between the Lyapunov–Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems

The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov–Krasovskii approach. In the networked control systems domain a similar delay stability problem is treated using a switched system transformation ap...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems 2008-08, Vol.2 (3), p.697-705
Main Authors: Hetel, L., Daafouz, J., Iung, C.
Format: Article
Language:English
Subjects:
LMI
Lyapunov–Krasovskii functionals
Multiple Lyapunov functions
Switched systems
Time delay systems
Time varying delays
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Summary:The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov–Krasovskii approach. In the networked control systems domain a similar delay stability problem is treated using a switched system transformation approach. The paper aims to establish a relation between the switched system transformation approach and the classical Lyapunov–Krasovskii method. It is shown that using the switched systems transformation is equivalent to using a general delay dependent Lyapunov–Krasovskii functionals. This functional represents the most general form that can be obtained using sums of quadratic terms. Necessary and sufficient LMI conditions for the existence of such functionals are presented.
ISSN:1751-570X
DOI:10.1016/j.nahs.2007.11.003