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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 489-504. doi: 10.3934/mbe.2023022
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Reachability of dimension-bounded linear systems

  • 1.
    School of Mathematics, Shandong University, Jinan 250100, China
  • 2.
    School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
  • 3.
    School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
  • Received: 25 June 2022 Revised: 11 September 2022 Accepted: 23 September 2022 Published: 11 October 2022

  • 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.

    Citation: Yiliang Li, Haitao Li, Jun-e Feng, Jinjin Li. Reachability of dimension-bounded linear systems[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 489-504. doi: 10.3934/mbe.2023022

    Related Papers:

  • 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.


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