Output Feedback Pole Assignment for Transfer Functions with Symmetries

2005/11/04 by Uwe Helmke, Helmke, Uwe, Joachim Rosenthal +3
Mathematics · #14M15 #15A18 #70H14 #93B55 #93B60 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:14M15 #msc:15A18 #msc:70H14 #msc:93B55 #msc:93B60

paper · pdf · doi:10.48550/arxiv.math/0511112

18 pages

arxiv created 2005/11/04 · arxiv updated 2009/12/01

Abstract

This paper studies the problem of pole assignment for symmetric and Hamiltonian transfer functions. A necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given. Moreover, in the case where the McMillan degree coincides with the number of parameters appearing in the symmetric feedback transformations, we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains. The proof uses intersection theory in projective space as well as a formula for the degree of the complex Lagrangian Grassmann manifold.

Related

• Complex static skew-symmetric output feedback control
• Output Feedback Invariants
• On Symmetries in Analytic Input-Output Systems
• A Local Parametrization of the State-Feedback Matrices in the Pole Assignment Problem
• Quaternionic Pole Placement via Companion Forms and the Ackermann Formula