Reachability of Dimension-Bounded Linear Systems
Abstract
In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging the reachability of a given vector space is proposed. In addition, this paper proves that the t-step reachable subset is a linear space, and gives a computing method. The t-step reachability of a given state is verified via a rank condition. Furthermore, annihilator polynomials are discussed and used to illustrate the relationship between the invariant space and the reachable subset after the invariant time point t*. The inclusion relation between reachable subsets at times t*+i and t*+j is shown via an example.
Cite
@article{arxiv.2108.03889,
title = {Reachability of Dimension-Bounded Linear Systems},
author = {Yiliang Li and Haitao Li and Jun-e Feng and Jinjin Li},
journal= {arXiv preprint arXiv:2108.03889},
year = {2021}
}