A Periodic Dichotomy in Linear Control Theory
Optimization and Control
2026-04-07 v1
Abstract
In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic linear quadratic optimal control problems. Specifically, we establish a complete characterization of the optimal extremal under suitable exponential stabilizability and detectability assumptions.
Cite
@article{arxiv.2604.04003,
title = {A Periodic Dichotomy in Linear Control Theory},
author = {Shichao Ye and Xingwu Zeng and Can Zhang},
journal= {arXiv preprint arXiv:2604.04003},
year = {2026}
}
Comments
11 pages, 12 figures