Necessary and sufficient conditions for the controllability of linear interval descriptor systems
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the controllability of linear interval descriptor systems
zbMATH Open document ID: 0908.93012
DOI: 10.1016/S0005-1098(97)00204-5
author: Chong Lin
author: Jian-Liang Wang
author: Cheong Boon Soh
published in: Automatica
publication date: 1999-03-09T00:00:00Z
review text: The authors consider the linear, continuous-time descriptor system \[ \begin{aligned} E\dot x(t) &= Ax(t) + Bu(t),\\ y(t) &= Cx(t),\end{aligned} \] where \(x(t)\in\mathbb R^n,\) \(u(t)\in\mathbb R^p\) and \(y(t)\in\mathbb R^q\) are the state, input and output vectors, respectively; \(E, A\in\mathbb R^{n\times n}, B\in\mathbb R^{n\times p}\) and \(C\in\mathbb R^{q\times n}\) are system matrices. Here, \(B\) and \(C\) are of full column and row rank, respectively; \(E\) may be singular (i.e. rank \(E\leq n\)). In this paper, the regularity and controllability of the descriptor system with interval drift are investigated, i.e., \(A\) is an \(n\times n\) interval matrix which represents plant uncertainties. Sufficient conditions for controllability of all the systems \((E, A + \Delta A, B)\) are derived. Necessary and sufficient conditions for regularity and controllability of the system with interval drift are established. Three numerical examples are given to illustrate the obtained results.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1192892
zbMATH Keywords: descriptor systems
zbMATH Keywords: interval plants
zbMATH Keywords: robustness
zbMATH Keywords: controllability
zbMATH Keywords: regularity
zbMATH Keywords: impulse behavior
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1192892