Rational matrix structure
- 1 April 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 26 (2), 434-439
- https://doi.org/10.1109/tac.1981.1102593
Abstract
We bring together in this paper, in a unified way, certain results developed by various people regarding the pole/zero structure of a rational matrix and the structure of the vector-space generated by its columns. Pole and zero structure, at finite and infinite arguments, is compactly described by using elementary ideas from the language of valuation theory. The concept of column-reducedness of a rational matrix at some argument is introduced, and shown to determine when its pole/zero structure is simply that of its columns taken separately. We describe a procedure that operates on the Laurent expansion of a given rational matrix at the argument of interest in order to transform the matrix to one that is column-reduced at this argument but has the same pole/zero structure. The occurrence of such a "structure-extraction" algorithm in various contexts in system theory is pointed out. Special properties of rational bases (for a rational vector space) that are column-reduced at all arguments are noted, somewhat extending what is already well-known for minimal polynomial bases for such a space.Keywords
This publication has 12 references indexed in Scilit:
- A generalized state-space for singular systemsIEEE Transactions on Automatic Control, 1981
- Properties of the system matrix of a generalized state-space system†International Journal of Control, 1979
- On the determination of the Smith-Macmillan form of a rational matrix from its Laurent expansionIEEE Transactions on Circuits and Systems, 1979
- Minimal Factorization of Matrix and Operator FunctionsPublished by Springer Science and Business Media LLC ,1979
- A local I/O structure theory for multivariable systems and its application to minimal cascade realizationIEEE Transactions on Circuits and Systems, 1978
- Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear SystemsSIAM Journal on Control, 1975
- Linear Multivariable SystemsApplied Mathematical Sciences, 1974
- A minimization algorithm for the design of linear multivariable systemsIEEE Transactions on Automatic Control, 1973
- Inversion of multivariable linear systemsIEEE Transactions on Automatic Control, 1969
- Introduction to Formal Realizability Theory-IIBell System Technical Journal, 1952