2019/12/09 by Roberta Fabbri, Fabbri, Roberta, Carmen Núñez +1
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1912.03940
The Yakubovich Frequency Theorem, in its periodic version and in its general\nnonautonomous extension, establishes conditions which are equivalent to the\nglobal solvability of a minimization problem of infinite horizon type, given by\nthe integral in the positive half-line of a quadratic functional subject to a\ncontrol system. It also provides the unique minimizing pair "solution, control"\nand the value of the minimum. In this paper we establish less restrictive\nconditions under which the problem is partially solvable, characterize the set\nof initial data for which the minimum exists, and obtain its value as well a\nminimizing pair. The occurrence of exponential dichotomy and the null character\nof the rotation number for a nonautonomous linear Hamiltonian system defined\nfrom the minimization problem are fundamental in the analysis.\n