Technical communique: All doubly coprime factorizations of a general rational matrix

Authors:
Cristian Oar;Şerban Sabu
Affiliations:
Faculty of Automatic Control and Computers, University "Politehnica" Bucharest, Splaiul Independenei 313, sector 6, RO 060042, Bucharest, Romania;Electrical Engineering Department, University of Maryland at College Park, A.V. Williams Bldg., Rm. 2248, College Park, MD 20783, USA
Venue:
Automatica (Journal of IFAC)
Year:
2009

Citing 5
Cited 0

An algorithm for inverting rational matrices

Systems & Control Letters
Robust and optimal control

Robust and optimal control
Minimal Degree Coprime Factorization of Rational Matrices

SIAM Journal on Matrix Analysis and Applications
Technical Communique: Doubly coprime factorizations related to any stabilizing controllers in state space

Automatica (Journal of IFAC)
Brief Bezout identity related to reduced-order observer-based controllers for singular systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.14

Visualization

Abstract

For a general rational matrix function (possibly polynomial or improper) we give state-space formulas for the class of all doubly coprime factorizations over an arbitrary fixed set in the closed complex plane. The main result is expressed in terms of a special type of realization-called centered-that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the proper case. In particular, the formulas can be specialized to get the parametrization of all proper, polynomial, or proper and stable doubly coprime factorizations of an arbitrary descriptor system. En route, we provide a closed state-space formula for the inverse of an invertible general rational matrix.