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Pole Assignment for Symmetric Quadratic Dynamical Systems: An Algorithmic Method

Pantazopoulou, S., Tomas-Rodriguez, M. ORCID: 0000-0001-9630-9579, Kalogeropoulos, G. & Halikias, G. (2024). Pole Assignment for Symmetric Quadratic Dynamical Systems: An Algorithmic Method. Paper presented at the 28th International Conference on Circuits, Systems, Communications and Computers (CSCC), 19-22 Jul 2024, Heraklion, Crete Island, Greece.


In this article an algorithmic method is proposed for the solution of the pole assignment problem which is associated with a symmetric quadratic dynamical system, in case it is completely controllable. The above problem is proved to be equivalent to two subproblems, one linear and the other multilinear. Solutions of the linear problem must be decomposable vectors, i.e. they must lie in an appropriate Grassmann variety. The proposed method computes a reduced set of quadratic Plucker relations with only three terms each, which describe completely the specific Grassmann variety. Using these relations one can solve the multilinear problem and consequently calculate the feedback matrices which give a solution to the pole assignment problem. Finally, an illustrative example of the proposed algorithmic procedure is given.The advantage of this approach, is that the complete set of feedback solutions is obtained, over which further optimisation can be carried out, if desired.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: © 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publisher Keywords: Control Theory, Pole assignment, Quadratic matrix pencils, Grassmann variety, Plucker relations, numerical algorithm
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology
School of Science & Technology > Engineering
SWORD Depositor:
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