Robust stabilisation of time-varying delay systems with probabilistic uncertainties

For robust stabilisation of time-varying delay systems, only sufficient conditions are available to date. A natural question is as follows: if the existing sufficient conditions are not satisfied, and hence no controllers can be found, what can one do to improve the stability performance of time-var...

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Bibliographic Details
Published in:International journal of systems science Vol. 47; no. 12; pp. 3016 - 3026
Main Authors: Jiang, Ning, Xiong, Junlin, Lam, James
Format: Journal Article
Language:English
Published: Taylor & Francis 09.09.2016
Subjects:
Controllers
Delay
Design analysis
Design engineering
Mathematical models
Probabilistic methods
probabilistic uncertain parameters
Probability theory
randomised algorithms
robust stabilisation
time-varying delay systems
Uncertainty
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:For robust stabilisation of time-varying delay systems, only sufficient conditions are available to date. A natural question is as follows: if the existing sufficient conditions are not satisfied, and hence no controllers can be found, what can one do to improve the stability performance of time-varying delay systems? This question is addressed in this paper when there is a probabilistic structure on the parameter uncertainty set. A randomised algorithm is proposed to design a state-feedback controller, which stabilises the system over the uncertainty domain in a probabilistic sense. The capability of the designed controller is quantified by the probability of stability of the resulting closed-loop system. The accuracy of the solution obtained from the randomised algorithm is also analysed. Finally, numerical examples are used to illustrate the effectiveness and advantages of the developed controller design approach.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2015.1063173