Complex Static Skew-Symmetric Output Feedback Control Academic Article uri icon


  • 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 complex feedback laws when there are finitely many of them. Finally, we also construct a real skew-symmetric linear system with only real feedback for any set of real poles. 2013 Society for Industrial and Applied Mathematics.

published proceedings

  • SIAM Journal on Control and Optimization

author list (cited authors)

  • Hillar, C. J., & Sottile, F.

citation count

  • 2

complete list of authors

  • Hillar, Christopher J||Sottile, Frank

publication date

  • January 2013