Weak asymptotic stabilizability of discrete-time systems given by set-valued operators
type: Item
instance of: scholarly article
title: Weak asymptotic stabilizability of discrete-time systems given by set-valued operators
zbMATH Open document ID: 0858.93055
author: V. N. Phat
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-11-13T00:00:00Z
review text: Let \(T\) be a convex process in a Banach space \(X\) (i.e. \(T\) is a multioperator whose graph is a closed convex cone). A discrete inclusion \[ x(k+1)\in T(x(k)), \qquad k=0,1,\dots \] is said to be weakly asymptotically stabilizable if for every \(x_0\in X\) there is a solution \(x(k)\) such that \(x(0)=x_0\) and \(x(k)\to0\) as \(k\to\infty\). The author characterizes spectral properties of closed convex multioperators in Banach space. On that base, sufficient conditions for weak asymptotic stabilizability of discrete inclusions in terms of controllability-like conditions are given. The results are applied to the study of linear discrete control systems of the form \[ x(k+1)= Ax(k)+Bu(k), \qquad u(k)\in\Omega. \]
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 930196
zbMATH Keywords: multivalued map
zbMATH Keywords: discrete inclusion
zbMATH Keywords: spectral properties
zbMATH Keywords: multioperators in Banach space
zbMATH Keywords: asymptotic stabilizability
zbMATH Keywords: controllability
zbMATH Keywords: linear
zbMATH Keywords: discrete control systems
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0321
OpenAlex ID: W1971650550
DOI: 10.1006/JMAA.1996.0321
description: scientific article; zbMATH DE number 930196