Solvability, Controllability, and Observability of Continuous Descriptor Systems

Elizabeth L. Yip, Richard F. Sincovec

Research output: Contribution to journalArticle

322 Citations (Scopus)

Abstract

In this paper, we investigate the properties of the continuous descriptor system [formulla omitted] where E, A, and B are complex and possibly singular matrices and u(t) is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.

Original languageEnglish (US)
Pages (from-to)702-707
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume26
Issue number3
DOIs
StatePublished - Jun 1981

Fingerprint

Observability
Controllability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

Solvability, Controllability, and Observability of Continuous Descriptor Systems. / Yip, Elizabeth L.; Sincovec, Richard F.

In: IEEE Transactions on Automatic Control, Vol. 26, No. 3, 06.1981, p. 702-707.

Research output: Contribution to journalArticle

Yip, Elizabeth L. ; Sincovec, Richard F. / Solvability, Controllability, and Observability of Continuous Descriptor Systems. In: IEEE Transactions on Automatic Control. 1981 ; Vol. 26, No. 3. pp. 702-707.
@article{2fa5a38ee5d14cd8a281bf4ae37ec12a,
title = "Solvability, Controllability, and Observability of Continuous Descriptor Systems",
abstract = "In this paper, we investigate the properties of the continuous descriptor system [formulla omitted] where E, A, and B are complex and possibly singular matrices and u(t) is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.",
author = "Yip, {Elizabeth L.} and Sincovec, {Richard F.}",
year = "1981",
month = "6",
doi = "10.1109/TAC.1981.1102699",
language = "English (US)",
volume = "26",
pages = "702--707",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Solvability, Controllability, and Observability of Continuous Descriptor Systems

AU - Yip, Elizabeth L.

AU - Sincovec, Richard F.

PY - 1981/6

Y1 - 1981/6

N2 - In this paper, we investigate the properties of the continuous descriptor system [formulla omitted] where E, A, and B are complex and possibly singular matrices and u(t) is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.

AB - In this paper, we investigate the properties of the continuous descriptor system [formulla omitted] where E, A, and B are complex and possibly singular matrices and u(t) is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.

UR - http://www.scopus.com/inward/record.url?scp=0019579160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019579160&partnerID=8YFLogxK

U2 - 10.1109/TAC.1981.1102699

DO - 10.1109/TAC.1981.1102699

M3 - Article

AN - SCOPUS:0019579160

VL - 26

SP - 702

EP - 707

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 3

ER -