On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays.
type: Item
instance of: scholarly article
title: On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays.
zbMATH Open document ID: 1036.93054
DOI: 10.1016/S0096-3003(03)00224-8
author: D. Massart
published in: Applied Mathematics and Computation
publication date: 2004-03-14T00:00:00Z
review text: The following controlled system is considered \[ \begin{multlined} \dot{x}(t)=A_{0}x(t)+\sum_{k=1}^{r}A_{k}x(t-h_{k}(t))+\Delta F_{x}(t,x(t)),x(t-h_{1}(t)),\dots,x(t-h_{k}(t))+\\ Bu(t)+\Delta F_{u}(t,u(t)),\quad t \in [0,\infty],\;x(t)=\theta(t),\;t \in [-H,0],\end{multlined} \] with a feedback controller \[ u(t)=-Kx(t) \] and with the cost function \[ \int_{0}^{\infty}(x^{T}(t)Qx(t)+u^{T}(t)Su(t))\,dt. \] Here \(\Delta F_{x}\) and \(\Delta F_{u}\) are unknown perturbations with conditions \[ \| \Delta F(t,z_{0},\dots,z_{r})\| \leqslant \sum_{k=0}^{r}\alpha_{k}\| z_{k}\| ,\| \Delta F(t,z)\| \leqslant \beta \| z\| ; \] \(0\leqslant h_{k}(t)\leqslant h_{k}<\infty,\dot{h}_{k}(t)\leqslant h_{2k}<1,H=(h_1,\dots,h_r).\) Under LMI conditions, the authors prove that closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function.
reviewed by: T. Tadumadze
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 2056343
zbMATH Keywords: nonfragile guaranteed cost control
zbMATH Keywords: multiple time delays
zbMATH Keywords: Lyapunov method
zbMATH Keywords: linear matrix inequality
zbMATH Keywords: robust stabilization
zbMATH Keywords: perturbations
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
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full work available at URL: s0096-3003(03)00224-8
OpenAlex ID: W2140492949
description: scientific article; zbMATH DE number 2056343