Solvability, Controllability, and Observability of Continuous Descriptor Systems

Elizabeth L. Yip, Richard F. Sincovec

Research output: Contribution to journalArticlepeer-review

362 Scopus citations


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
Issue number3
StatePublished - Jun 1981

ASJC Scopus subject areas

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


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