Sufficient conditions for robust stability of linear nonstationary control systems with periodic interval constraints
type: Item
instance of: scholarly article
title: Sufficient conditions for robust stability of linear nonstationary control systems with periodic interval constraints
zbMATH Open document ID: 0928.93043
author: M. V. Morozov
author: Alexander Molchanov
published in: Automation and Remote Control
publication date: 2000-01-02T00:00:00Z
review text: The authors consider a linear nonstationary control system of the form \[ \dot x = A(t)x,\quad x \in R^n \] where \(A(t)\) is an \(n \times n\)-matrix function satisfying a.e. on each bounded interval of the semiaxis \([0,\infty)\) the following constraints: \(\underline A(t) \leq A(t) \leq \bar A(t)\) where the given bounded measurable matrix functions \(\underline A(t)\) and \(\bar A(t)\) are assumed to be periodic. The system is said to be robust stable with respect to given periodic constraints provided its zero solution is Lyapunov asymptotically stable for any choice of a matrix function \(A(t)\) satisfying the given constraints. Sufficient conditions for robust stability are given on the base of the method of comparison with a Lyapunov vector function of a special form. It is demonstrated that these conditions are also necessary under some additional assumptions. The results are generalized to the case of linear control systems with polyhedral periodic constraints.
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C99
zbMATH DE Number: 1290216
zbMATH Keywords: robust stability
zbMATH Keywords: linear control system
zbMATH Keywords: periodic constraints
zbMATH Keywords: time-varying
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1290216