\(H_\infty\) control of discrete-time linear systems with time-varying delays in state
type: Item
instance of: scholarly article
title: \(H_\infty\) control of discrete-time linear systems with time-varying delays in state
zbMATH Open document ID: 0936.93019
DOI: 10.1016/S0005-1098(99)00057-6
author: Seong-Ho Song
author: Jeom-Keun Kim
author: Choong-Hyuk Yim
author: Ho-Chan Kim
published in: Automatica
publication date: 1999-10-27T00:00:00Z
review text: This paper is concerned with the \(H_\infty\) control of discrete-time linear systems with time-varying delays. The main result shows that if the system \[ \begin{aligned} x_{k+1} & = A_1x_k+ B_1u_k+ [A_2Q^{-1/2} \gamma^{-1} B_2]w_k,\\ z_k & = \Biggl[\begin{matrix} \sqrt mQ^{-1/2}\\ C\end{matrix}\Biggr] x_k+ \Biggl[\begin{matrix} 0\\ D\end{matrix}\Biggr] u_k\end{aligned} \] is quadratically stabilizable with a unitary \(H_\infty\) norm-bound, then the system \[ \begin{aligned} x_{k+1} & = A_1 x_k+ B_1 u_k+ B_2w_k,\\ z_k & = Cx_k+ Du_k\end{aligned} \] is stabilizable with an \(H_\infty\) norm-bound \(\gamma\) by the same control law. The proof is based on fairly standard linear matrix inequalities and Lyapunov theory.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 1353728
zbMATH Keywords: quadratic stabilization
zbMATH Keywords: \(H_\infty\) control
zbMATH Keywords: discrete-time linear systems
zbMATH Keywords: time-varying delays
zbMATH Keywords: linear matrix inequalities
reviewed by: S. P. Banks
MaRDI profile type: Publication
full work available at URL: s0005-1098(99)00057-6
OpenAlex ID: W2048344004
description: scientific article; zbMATH DE number 1353728