Dwell time-based stabilisation of switched delay systems using free-weighting matrices

Date
2018
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Source Title
International Journal of Control
Print ISSN
0020-7179
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Publisher
Taylor and Francis
Volume
91
Issue
1
Pages
1 - 11
Language
English
Type
Article
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Abstract

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities, dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.

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Keywords
Dwell time optimisation, Free-weighting matrices, Switched delay systems, Time-delay
Citation
Published Version (Please cite this version)