Journal
NONLINEAR ANALYSIS-HYBRID SYSTEMS
Volume 2, Issue 3, Pages 697-705Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.nahs.2007.11.003
Keywords
Time delay systems; Switched systems; Time varying delays; Lyapunov-Krasovskii functionals; Multiple Lyapunov functions; LMI
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Funding
- HYCON Network of Excellence [FP6-IST-511368]
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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. (c) 2007 Elsevier Ltd. All rights reserved.
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