Optimal ellipsoidal bounds of the reachable set of linear systems with an uncertain matrix
type: Item
instance of: scholarly article
title: Optimal ellipsoidal bounds of the reachable set of linear systems with an uncertain matrix
zbMATH Open document ID: 0907.93007
author: D. Ya. Rokityanskij
published in: Journal of Computer and Systems Sciences International
publication date: 1998-08-03T00:00:00Z
review text: The linear dynamical system \[ \dot x = (A_0 (t) + A(t))x + w(t), \quad w(t) \in E_1, \quad x_0\in E_0 , \] \[ A(t) \in M(t) = \{ A \subset M_n : | | A| | _{\alpha} \leq h \} , \] is considered. Here \(E_0 = E(a_0, Q_0)\) and \(E_1 = E(c,B)\) are ellipsoids in \(R^n\) and \(| | A| | _{\alpha}\) is a norm in the space \(M_n\) of \(n\times n\) -matrices. The author finds the upper ellipsoidal bounds \(E(a(t),Q(t))\), \[ E(a(t),Q(t)) \supset D(t), \] of the attainable sets \(D(t)\) of the system for some types of norms \(| | A| | _{\alpha}\). The differential equations for the centers \(a(t)\) and for the matrices \(Q(t)\) of the ellipsoids that define the upper bounds are given.
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C41
zbMATH DE Number: 1158011
zbMATH Keywords: uncertainty
zbMATH Keywords: ellipsoidal bounds
zbMATH Keywords: attainable set
reviewed by: T. F. Filippova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1158011