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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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
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Abstract 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.
AbstractList 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.
Author Xiong, Junlin
Lam, James
Jiang, Ning
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  organization: Department of Mechanical Engineering, University of Hong Kong
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crossref_primary_10_1016_j_jfranklin_2021_09_011
crossref_primary_10_1080_00207721_2018_1536233
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SubjectTerms Controllers
Delay
Design analysis
Design engineering
Mathematical models
Probabilistic methods
probabilistic uncertain parameters
Probability theory
randomised algorithms
robust stabilisation
time-varying delay systems
Uncertainty
Title Robust stabilisation of time-varying delay systems with probabilistic uncertainties
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