eprintid: 2477
rev_number: 6
eprint_status: archive
userid: 6
dir: disk0/00/00/24/77
datestamp: 2015-01-13 14:34:09
lastmod: 2015-11-02 09:57:27
status_changed: 2015-01-13 14:34:09
type: article
metadata_visibility: show
creators_name: Cerone, Vito
creators_name: Piga, Dario
creators_name: Regruto, Diego
creators_id: 
creators_id: dario.piga@imtlucca.it
creators_id: 
title: Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: robust coprimeness, robust characteristic polynomial assignment, semialgebraic uncertainty, sum-of-square decomposition
note: Article first published online: 9 SEP 2014
abstract: In this paper, we address the problem of robust characteristic polynomial assignment for LTI systems whose parameters are assumed to belong to a semialgebraic uncertainty region. The objective is to design a dynamic fixed-order controller in order to constrain the coefficients of the closed-loop characteristic polynomial within prescribed intervals. First, necessary conditions on the plant parameters for the existence of a robust controller are reviewed, and it is shown that such conditions are satisfied if and only if a suitable Sylvester matrix is nonsingular for all possible values of the uncertain plant parameters. The problem of checking such a robust nonsingularity condition is formulated in terms of a nonconvex optimization problem. Then, the set of all feasible robust controllers is sought through the solution to a suitable robust diophantine equation. Convex relaxation techniques based on sum-of-square decomposition of positive polynomials are used to efficiently solve the formulated optimization problems by means of semidefinite programming. The presented approach provides a generalization of the results previously proposed in the literature on the problem of assigning the characteristic polynomial in the presence of plant parametric uncertainty.
date: 2014
date_type: published
publication: International Journal of Robust and Nonlinear Control 
volume: 25
number: 16
publisher: Wiley-Blackwell
pagerange: 2911-2921
id_number: 10.1002/rnc.3238
refereed: TRUE
issn: 1049-8923
official_url: http://dx.doi.org/10.1002/rnc.3238
citation:   Cerone, Vito and Piga, Dario and Regruto, Diego  Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach.  International Journal of Robust and Nonlinear Control , 25 (16).  pp. 2911-2921.  ISSN 1049-8923      (2014)