Robust simple adaptive model following for linear time-delay systems with guaranteed H performance

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)475-491
Number of pages17
JournalIMA Journal of Mathematical Control and Information
Issue number4
StatePublished - Dec 2010


  • H performance
  • adaptive control
  • simple adaptive control
  • time-delay systems


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