@article{eprints2477,
         journal = {International Journal of Robust and Nonlinear Control },
       publisher = {Wiley-Blackwell},
            note = {Article first published online: 9 SEP 2014},
          author = {Vito Cerone and Dario Piga and Diego Regruto},
          volume = {25},
          number = {16},
           pages = {2911--2921},
           title = {Characteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approach},
            year = {2014},
             url = {http://eprints.imtlucca.it/2477/},
        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.},
        keywords = {robust coprimeness, robust characteristic polynomial assignment, semialgebraic uncertainty, sum-of-square decomposition}
}