Static skew-symmetric output feedback control

Details Static skew-symmetric output feedback control Static skew-symmetric output feedback control

2011-11-15

arxiv.org/abs/1111.3501v1

Mathematics

Optimization and Control

16 pages

Scientific paper

We study the problem of feedback control for skew-symmetric and skew-Hamiltonian transfer functions using skew-symmetric controllers. This extends work of Helmke, et al., who studied static symmetric feedback control of symmetric and Hamiltonian linear systems. We identify spaces of linear systems with symmetry as natural subvarieties of the moduli space of rational curves in a Grassmannian, give necessary and sufficient conditions for pole placement by static skew-symmetric complex feedback, and use Schubert calculus for the orthogonal Grassmannian to count the number of feedback laws when there are finitely many. Finally, we also construct a skew-symmetric linear system and poles with only real feedback laws.

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