Greatest common divisor via generalized Sylvester and Bezout matrices
- 1 December 1978
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 23 (6) , 1043-1047
- https://doi.org/10.1109/tac.1978.1101890
Abstract
We present new methods for computing the greatest common right divisor of polynomial matrices. These methods involve the recently studied generalized Sylvester and generalized Bezoutian resultant matrices, which require no polynomial operations. They can provide a row proper greatest common right divisor, test for coprimeness and calculate dual dynamical indices. The generalized resultant matrices are developments of the scalar Sylvester and Bezoutian resultants and many of the familiar properties of these latter matrices are demonstrated to have analogs with the properties of the generalized resultant matrices for matrix polynomials.Keywords
This publication has 16 references indexed in Scilit:
- An algorithm for obtaining the minimal realization of a linear time-invariant system and determining if a system is stabilizable-detectablePublished by Institute of Electrical and Electronics Engineers (IEEE) ,1977
- New criteria and system theoretic interpretations for relatively prime polynomial matricesIEEE Transactions on Automatic Control, 1977
- A generalized resultant matrix for polynomial matricesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1976
- Resultants of matrix polynomialsBulletin of the American Mathematical Society, 1976
- Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear SystemsSIAM Journal on Control, 1975
- Linear Multivariable SystemsPublished by Springer Nature ,1974
- A minimization algorithm for the design of linear multivariable systemsIEEE Transactions on Automatic Control, 1973
- Determination of the least order of transfer-function matricesProceedings of the Institution of Electrical Engineers, 1971
- Regular polynomial matrices having relatively prime determinantsMathematical Proceedings of the Cambridge Philosophical Society, 1969
- Generalised resultantElectronics Letters, 1968