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Characteristic polynomial assignment for plants with semialgebraic uncertainty: A robust diophantine equation approach.
- Source :
-
International Journal of Robust & Nonlinear Control . Nov2015, Vol. 25 Issue 16, p2911-2921. 11p. - Publication Year :
- 2015
-
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. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10498923
- Volume :
- 25
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- International Journal of Robust & Nonlinear Control
- Publication Type :
- Academic Journal
- Accession number :
- 110138532
- Full Text :
- https://doi.org/10.1002/rnc.3238