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PreprintCC BY 4.0arXiv

Determination of the output injection of invertible linear systems for guaranteeing a regular relative degree

  • Shida Cao
  • Bin Zhou
  • Guang-Ren Duan
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Abstract

For an invertible linear time-invariant system, the Morse normal form reveals that there exist an output injection and an output transformation such that the resulting system possesses a regular relative degree. Based on this fact, this paper develops a method to determine all admissible output injections and output transformations that achieve this property. In contrast to the recursive and implicit computation methods in the existing literature, the proposed determination method for the output injections is explicit and easy to use, since the solutions are obtained by solving linear matrix equations. A rigorous proof of the proposed method is provided, and an illustrative example is presented to demonstrate the applicability of the approach.

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Cite

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BibTeX
@misc{cao2026determination,
  title = {{Determination of the output injection of invertible linear systems for guaranteeing a regular relative degree}},
  author = {Shida Cao and Bin Zhou and Guang-Ren Duan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20018},
  eprint = {2609.20018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20018},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Determination of the output injection of invertible linear systems for guaranteeing a regular relative degree
AU  - Shida Cao
AU  - Bin Zhou
AU  - Guang-Ren Duan
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20018
UR  - https://arxiv.org/abs/2609.20018
AB  - For an invertible linear time-invariant system, the Morse normal form reveals that there exist an output injection and an output transformation such that the resulting system possesses a regular relative degree. Based on this fact, this paper develops a method to determine all admissible output injections and output transformations that achieve this property. In contrast to the recursive and implicit computation methods in the existing literature, the proposed determination method for the output injections is explicit and easy to use, since the solutions are obtained by solving linear matrix equations. A rigorous proof of the proposed method is provided, and an illustrative example is presented to demonstrate the applicability of the approach.
ER  -