Higher-Order Singular Systems and Polynomial Matrices

The Correspondence between Quadruples of Matrices and Polynomial Matrices in Higher-Order Singular Systems

Abstract

There is aone-to-one correspondence between the set of quadruples of matricesdefiningsingular linear time-invariant dynamical systems and a subset of the set ofpolynomial matrices. This correspondence preserves the equivalence relationsintroduced in both sets (feedback-similarity and strict equivalence): twoquadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are alsostrictly equivalent.