Perturbation theory of observable linear systems
Abstract
The present work is motivated by the asymptotic control theory for a system of linear oscillators: the problem is to design a common bounded scalar control for damping all oscillators in asymptotically minimal time. The motion of the system is described in terms of a canonical system similar to that of the Pontryagin maximum principle. We consider the evolution equation for adjoint variables as a perturbed observable linear system. Due to the perturbation, the unobservable part of the state trajectory cannot be recovered exactly. We estimate the recovering error via the -norm of perturbation. This allows us to prove that the control makes the system approach the equilibrium state with a strictly positive speed.
Keywords
Cite
@article{arxiv.1404.6901,
title = {Perturbation theory of observable linear systems},
author = {Aleksey Fedorov and Alexander Ovseevich},
journal= {arXiv preprint arXiv:1404.6901},
year = {2015}
}
Comments
7 pages; the subject of the present paper has grown out of study arXiv:1308.6090 (see Appendix V); published version