WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 19, 2024
Pole Assignment for Symmetric Quadratic Dynamical Systems: An
Algorithmic Method
Authors: S. Pantazopoulou, M. Tomas-Rodriguez, G. Kalogeropoulos, G. Halikias
Abstract: 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, when it is completely controllable. The problem is
shown to be equivalent to two subproblems, one linear and the other multi-linear. 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 multi-linear problem and consequently
calculate the feedback matrices which give a solution to the pole assignment problem. An illustrative example
of the proposed algorithmic procedure is given. The main advantage of our approach is that the complete set of
feedback solutions is obtained, over which further optimisation can be carried out, if desired. This is important
for problems with structural constraints (e.g. decentralization) or norm-constraints on the feedback gain-matrix.
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Keywords: Control Theory, Pole assignment, Quadratic matrix pencils, Grassmann variety, Plucker relations,
numerical algorithm
Pages: 227-233
DOI: 10.37394/23203.2024.19.24
WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 19, 2024, Art. #24