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Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach

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)

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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.

Item Type: Article
Identification Number: 10.1002/rnc.3238
Additional Information: Article first published online: 9 SEP 2014
Uncontrolled Keywords: robust coprimeness, robust characteristic polynomial assignment, semialgebraic uncertainty, sum-of-square decomposition
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 13 Jan 2015 14:34
Last Modified: 02 Nov 2015 09:57
URI: http://eprints.imtlucca.it/id/eprint/2477

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