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arXiv · 2108.03889

Reachability of Dimension-Bounded Linear Systems

Yiliang Li·Haitao Li·Jun-e Feng·Jinjin Li
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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.

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Yiliang Li, Haitao Li, Jun-e Feng, Jinjin Li. 2021-08-09. Reachability of Dimension-Bounded Linear Systems. https://arxiv.org/abs/2108.03889

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