Dynamical methods for linear Hamiltonian systems with applications to control process,

with Russell Johnson and Rafael Obaya,
J. Dynam. Differential Equations, 25 (3) (2013), 679-713.


The nonautonomous version of the Yakubovich Frequency Theorem characterizes

the solvability of an infinite horizon optimization problem in terms of the validity of the

Frequency and Nonoscillation Conditions for a linear Hamiltonian system, which is defined

from the coefficients of the quadratic functional to be minimized. This paper describes those

nonautonomous linear Hamiltonian systems satisfying the required properties. Two groups

appear, depending on whether they are uniformly weakly disconjugate or not. It also contains

a previous analysis of the long-term behavior of the Grassmannian and Lagrangian flows

under the presence of exponential dichotomy, which is required for the classification and has

interest by itself.