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The feedback invariant measures of distance to uncontrollability and unobservability

Karcanias, N., Limantseva, O. ORCID: 0000-0003-2764-4415 and Halikias, G. ORCID: 0000-0003-1260-1383 (2020). The feedback invariant measures of distance to uncontrollability and unobservability. International Journal of Control, doi: 10.1080/00207179.2020.1845398

Abstract

The selection of systems of inputs and outputs forms part of the early system design that is important since it preconditions the potential for control design. Existing methodologies for input, output structure selection rely on criteria expressing distance to uncontrollability, unobservability. Although controllability is invariant under state feedback, its corresponding degrees expressing distance to uncontrollability is not. The paper introduces new criteria for distance to uncontrollability (dually for unobservability) which is invariant under feedback transformations. The approach uses the restricted matrix pencils developed for the characterisation of invariant spaces of the geometric theory and then deploys exterior algebra to define the invariant input and output decoupling polynomials. This reduces the overall problem of distance to uncontrollability (unobservability) to two optimisation problems: the distance from the Grassmann variety and distance of a set of polynomials from non-coprimeness. Results on the distance of Sylvester Resultants from singularity provide the new measures.

Publication Type: Article
Additional Information: This is an Accepted Manuscript version of the following article, accepted for publication in International Journal of Control. Nicos Karcanias, Olga Limantseva & George Halikias (2020) The feedback invariant measures of distance to uncontrollability and unobservability, International Journal of Control, DOI: 10.1080/00207179.2020.1845398. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords: Distance to uncontrollability, distance to unobservability, feedback invariant measures, decomposability of multivectors, Sylvester resultant, ‘approximate’ GCD
Subjects: Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 09 Dec 2020 09:24
URI: https://openaccess.city.ac.uk/id/eprint/25361
[img] Text - Accepted Version
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