DocumentCode :
2235791
Title :
Fast-lifting approach to time-delay systems: Fundamental framework
Author :
Hagiwara, Tomomichi
Author_Institution :
Dept. of Electr. Eng., Kyoto Univ., Kyoto, Japan
fYear :
2008
fDate :
9-11 Dec. 2008
Firstpage :
5292
Lastpage :
5299
Abstract :
This paper gives a novel approach to time-delay systems consisting of a linear time-invariant (LTI) system and a pure delay. The fast-lifting technique, introduced recently in the context of the study of sampled-data systems, is applied to the monodromy operator of a time-delay system to define the fast-lifted monodromy operator, and a stability condition is given in terms of the spectral radius of the latter operator. Then, by investigating the properties of this operator, an operator class described by two finite-dimensional matrices is introduced as candidates for a solution to the associated operator Lyapunov inequality. It is then established that the analysis restricted to such a class gives an asymptotically exact and nonconservative method for stability analysis if the integer N for fast-lifting is taken sufficiently large.
Keywords :
Lyapunov methods; delay systems; delays; linear systems; matrix algebra; sampled data systems; stability; Lyapunov inequality; fast-lifting approach; finite-dimensional matrix; linear time-invariant system; monodromy operator; sampled-data system; stability condition; time-delay system; Control systems; Delay; Differential equations; Linear matrix inequalities; Physiology; Robust stability; Stability analysis; Systems biology; Systems engineering and theory; Transportation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on
Conference_Location :
Cancun
ISSN :
0191-2216
Print_ISBN :
978-1-4244-3123-6
Electronic_ISBN :
0191-2216
Type :
conf
DOI :
10.1109/CDC.2008.4738609
Filename :
4738609
Link To Document :
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