Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field . We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of .
Title: On conjugate times of LQ optimal control problems
Authors: A.A. Agrachev, L. Rizzi, P. Silveira
Journal title: Dynamical and Control Systems
ArXiv ID (ENG): 1311.2009
MathNet (ENG): http://mi.mathnet.ru/eng/jdcs1