Dynamical Methods for Linear Hamiltonian Systems with Applications to Control Processes

摘要

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.