Approximate zero polynomials of polynomial matrices and linear systems

Karcanias, N. & Halikias, G. (2011). Approximate zero polynomials of polynomial matrices and linear systems. 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp. 465-470. doi: 10.1109/CDC.2011.6160302

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Abstract

This paper introduces the notions of approximate and optimal approximate zero polynomial of a polynomial matrix by deploying recent results on the approximate GCD of a set of polynomials [1] and the exterior algebra [4] representation of polynomial matrices. The results provide a new definition for the "approximate", or "almost" zeros of polynomial matrices and provide the means for computing the distance from non-coprimeness of a polynomial matrix. The computational framework is expressed as a distance problem in a projective space. The general framework defined for polynomial matrices provides a new characterization of approximate zeros and decoupling zeros [2], [4] of linear systems and a process leading to computation of their optimal versions. The use of restriction pencils provides the means for defining the distance of state feedback (output injection) orbits from uncontrollable (unobservable) families of systems, as well as the invariant versions of the "approximate decoupling polynomials".

Item Type: Article
Additional Information: © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/7297

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