TY  - JOUR
UR  - http://dx.doi.org/10.1002/rnc.3238
KW  - robust coprimeness
KW  -  robust characteristic polynomial assignment
KW  -  semialgebraic uncertainty
KW  -  sum-of-square decomposition
AV  - none
TI  - Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach
N2  - 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.
SN  - 1049-8923
EP  - 2921
N1  - Article first published online: 9 SEP 2014
ID  - eprints2477
JF  - International Journal of Robust and Nonlinear Control 
IS  - 16
Y1  - 2014///
SP  - 2911
PB  - Wiley-Blackwell
A1  - Cerone, Vito
A1  - Piga, Dario
A1  - Regruto, Diego
VL  - 25
ER  -