relation: http://eprints.imtlucca.it/2477/
title: Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach
creator: Cerone, Vito
creator: Piga, Dario
creator: Regruto, Diego
subject: QA75 Electronic computers. Computer science
description: 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.
publisher: Wiley-Blackwell
date: 2014
type: Article
type: PeerReviewed
identifier:   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)  
relation: http://dx.doi.org/10.1002/rnc.3238
relation: 10.1002/rnc.3238