Li Yiliang, Li Haitao, Feng Jun-E, Li Jinjin
School of Mathematics, Shandong University, Jinan 250100, China.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China.
Math Biosci Eng. 2023 Jan;20(1):489-504. doi: 10.3934/mbe.2023022. Epub 2022 Oct 11.
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 $ \mathcal{V}_{r} $ 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 employed to illustrate the relationship between the invariant space and the reachable subset after the invariant time point $ t^{\ast} $. The inclusion relation between reachable subsets at times $ t^{\ast}+i $ and $ t^{\ast}+j $ is shown via an example.
