Elsevier

Automatica

Volume 27, Issue 6, November 1991, Pages 985-995
Automatica

Paper
Minimality of descriptor representations under external equivalence

https://doi.org/10.1016/0005-1098(91)90133-MGet rights and content

Abstract

Necessary and sufficient conditions are derived for the minimality of descriptor representations under external equivalence. These conditions are stated completely in terms of the matrices E, A, B, C and D. Use is made of the close connection between the descriptor representation and the so-called pencil representation. This connection is further exploited to derive the transformation group for minimal descriptor representations. It is shown that the transformations coincide with the operations of strong equivalence as introduced by Verghese et al. (IEEE Trans. Aut. Control, AC-26, 811–831, 1981).

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The original version of this paper was presented at the IFAC Workshop on System Structure and Control: State Space and Polynomial Methods which was held in Prague, Czechoslovakia during September, 1989. The published proceedings of this IFAC Meeting may be ordered from Pergamon Press plc, Headington Hill Hall, Oxford OX3 0BW, U.K. This paper was recommended for publication in revised form by Associate Editor V. Kučera.

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