A New Approach of Adaptive H\Infty Control for a Class ofUncertain Nonlinear Time--Delay System with Multiple Time Delayand Uncertain Input Delay

Chai Lin;Fei Shumin

Journal of Systems Science and Mathematical Sciences ›› 2007, Vol. 27 ›› Issue (6) : 880-891.

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Journal of Systems Science and Mathematical Sciences ›› 2007, Vol. 27 ›› Issue (6) : 880-891. DOI: 10.12341/jssms10029
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A New Approach of Adaptive H\Infty Control for a Class ofUncertain Nonlinear Time--Delay System with Multiple Time Delayand Uncertain Input Delay

  • Chai Lin, Fei Shumin
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Abstract

A method of LMI, a kind of Lyapunov-Krasovskii functional, which is based on ``descriptor form", and a new type of memory state feedback controller are used to solve the problem of H∞ controller, designing new adaptive strategies for two unknown constant: input delay and up bound for norm of the uncertain nonlinear part. This type of strategy isn't limited in the estimate value as that of the old adaptive controllers and manages to avoid calculating ``adjusting constant", which guarantees the limitation as the old adaptive
controllers, by reflecting difference between the estimate value and the value being close to the practical. The sufficient condition of its solution is given with a numerical example.

Key words

Input delay / uncertain nonlinear part / multiple time delay / Lyapunov-Krasovskii functional based on ``descriptor form" / a new type of adaptive control / H∞.

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Chai Lin , Fei Shumin. A New Approach of Adaptive H\Infty Control for a Class ofUncertain Nonlinear Time--Delay System with Multiple Time Delayand Uncertain Input Delay. Journal of Systems Science and Mathematical Sciences, 2007, 27(6): 880-891 https://doi.org/10.12341/jssms10029
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