On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces

Authors

  • Elizaveta A. Kalinina St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Alexander M. Kamachkin St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Nikolai A. Stepenko St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Grigoriy Sh. Tamasyan Mozhaisky Military Space Academy, 13, Zhdanovskaya uh, St. Petersburg, 197082, Russian Federation; Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoy pr. V. O., St. Petersburg, 199178, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2023.213

Abstract

The rank of the Kalman’s controllability matrix of linear systems depends on the bases of the invariant cyclic subspaces of the state matrix generated by the columns of the input matrix. The case of the Jordan form of the state matrix and scalar control is studied in detail. It is shown that the dimension of cyclic subspaces is determined by the index numbers of the first non-zero elements of the coordinate blocks of the columns of the input matrix. The formation of the bases of these subspaces is completely disclosed. Based on this, the basis of the space of a constructive control system is constructed.

Keywords:

controllability, system structure, cyclic invariant subspaces

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References

Литература

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Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления

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Published

2023-07-27

How to Cite

Kalinina, E. A., Kamachkin, A. M., Stepenko, N. A., & Tamasyan, G. S. (2023). On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19(2), 283–299. https://doi.org/10.21638/11701/spbu10.2023.213

Issue

Vol. 19 No. 2 (2023)

Section

Control Processes

License

Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.