Subaggregation with linear observation maps
type: Item
instance of: scholarly article
title: Subaggregation with linear observation maps
zbMATH Open document ID: 0797.34013
author: Ladislav Lhotka
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-06-16T00:00:00Z
review text: The differential inclusion \(x'(t)\in F(x(t))\) together with the observation map \[ H(x)= \begin{cases} \{y\in\mathbb{R}^ q\mid Ax\leq y\} &\text{for }x\in K\\ \emptyset &\text{for }x\not\in K\end{cases} \] is considered. It is assumed that \(F\) is an upper semicontinuous set-valued map with non- empty convex and compact values and \(K\) is a closed set such that \(F(x)\cap T_ K(x)\neq \emptyset\) for each \(x\in K\). The map \(A\) is linear. Using the viability theory, a comparison system \(y'(t)= g(y(t))\) is constructed. The comparison system satisfies the following condition: For each pair of initial values \(x_ 0\in K\) and \(y_ 0\in H(x_ 0)\) there exists a solution \(x\) to the above differential inclusion and a solution \(y\) of the comparison system with \(y(0)= y_ 0\) such that for all \(t\geq 0\), \(y(t)\in H(x(t))\).
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 566438
zbMATH Keywords: differential inclusion
zbMATH Keywords: observation map
zbMATH Keywords: comparison system
reviewed by: Vlastimil Křivan
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1046
OpenAlex ID: W2048950744
DOI: 10.1006/JMAA.1994.1046
description: scientific article; zbMATH DE number 566438