Journal Article

Robust simple adaptive model following for linear time-delay systems with guaranteed <i>H<b><sub>∞</sub></b></i> performance

R. Ben Yamin, I. Yaesh and U. Shaked

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 27, issue 4, pages 475-491
Published in print December 2010 | ISSN: 0265-0754
Published online September 2010 | e-ISSN: 1471-6887 | DOI:
Robust simple adaptive model following for linear time-delay systems with guaranteed H∞ performance

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An output-feedback model-following problem is solved for linear time-varying delay systems with polytopic type parameter uncertainties and disturbances, using a simple direct adaptive control scheme with an additional proportional gain term, which is applied to the tracking error. The objective is to obtain sufficient conditions for closed-loop stability and guaranteed H performance of the proposed adaptive control scheme, so that the system output follows the output of the model. Sufficient conditions for closed-loop stability, model-following performance and prescribed H disturbance attenuation level of the proposed simple adaptive control scheme are given in terms of bilinear matrix inequalities. Stability is analysed using the Lyapunov–Krasovskii functional method, and both delay-dependent and delay-independent results are obtained. The proposed controller does not utilize the knowledge of the delay; only the bounds on the delay and the delay rate are used. Numerical examples are given, which demonstrate the effectiveness of the proposed controller and the simplicity of its implementation.

Keywords: adaptive control; time-delay systems; H∞ performance; simple adaptive control

Journal Article.  0 words. 

Subjects: Mathematics

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