Minimality of descriptor representations under external equivalence

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). © 1991.