Dynamic control for non-linear systems with delay
type: Item
instance of: scholarly article
title: Dynamic control for non-linear systems with delay
zbMATH Open document ID: 1263.34113
DOI: 10.3103/S1063454111030113
author: Irina Efremovna Zuber
author: Arkadiĭ Khaimovich Gelig
published in: Vestnik St. Petersburg University. Mathematics
publication date: 2012-11-21T00:00:00Z
review text: The paper is devoted to nonlinear systems with time-varying delay of the form \[ \dot x = A(\cdot)x + \sum_{i = 1}^l A_i (\cdot)x(t - \tau_i (t)) + b(\cdot)u, \] where \(A(\cdot) \in \mathbb{R}^{n \times n}\), \(A_i(\cdot) \in \mathbb{R}^{n \times n}\), \(b(\cdot) \in \mathbb{R}^n\), whose entries are arbitrary uniformly bounded functionals. For this class of systems, the authors derive sufficient conditions of existence and describe a method for reconstruction of a continuous or pulse dynamic control that makes the system globally asymptotically stable. Namely, a special type of the Lyapunov-Krasovskii functional is used to synthesize dynamic control described by the equation \[ \dot u = \rho (\cdot)u + (m(\cdot),x), \] where \(\rho (\cdot) \in \mathbb{R}^1\), \(m(\cdot) \in \mathbb{R}^n\).
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K29
zbMATH DE Number: 6109188
zbMATH Keywords: systems with time-varying delay
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: dynamic control
zbMATH Keywords: the Lyapunov-Krasovskii functional
MaRDI profile type: Publication
cites work: Robust invariant stabilization of nonlinear continuous and discrete systems
cites work: Robust stabilization of some class of uncertain systems
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: Q4210924
description: scientific article; zbMATH DE number 6109188