Robust stabilization of a class of nonlinear time-delay systems
type: Item
instance of: scholarly article
title: Robust stabilization of a class of nonlinear time-delay systems
zbMATH Open document ID: 1053.93037
DOI: 10.1016/S0096-3003(03)00813-0
author: Peng Shi
author: Changchun Hua
author: Xinping Guan
published in: Applied Mathematics and Computation
publication date: 2004-10-13T00:00:00Z
review text: The authors consider the controlled system \[ \dot{x} = Ax + Bu(t) + B\sum_{1}^r\eta_j(x(t-h_j(t)),t). \] Two feedback control laws are proposed: a) the memoryless adaptive controller \[ u = -(\mu/2)B^TPx - \overline{\theta}B^T(\partial V/\partial x)^T \] with \(P>0\) solution of the matrix Riccati equation \[ A^TP + PA + Q = \mu PBB^TP \] where \(Q>0\) and \(V(x) = \sum_{1}^s (1/i)(x^TPx)^i\); the adaptation law is given by \[ \dot{\overline{\theta}} = k| (\partial V/\partial x)B| ^2 - kl\overline{\theta} \] with \(k>0,l>0\) adjustable; b) the nonlinear feedback controller \[ u = - (1/2)(\mu+\nu)B^TPx - \rho(x)(B^TPx\rho(x))/(| B^TPx\rho(x)| +\vartheta\exp\{-\varepsilon t\}) \] \(\mu, P\) from the Riccati equation, \(\nu>0\) adjustable, \[ \rho(x) = \sum_{1}^s(\nu_i+\zeta_i| x(t)| )| x(t)| ^i \] and \(\nu_i>0\), \(\zeta_i>0\), \(\vartheta>0\) adjustable.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 2107378
zbMATH Keywords: time delay
zbMATH Keywords: adaptive control
zbMATH Keywords: nonlinear control
zbMATH Keywords: Riccati equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2107378