Geodesic
On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 339-358 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For block matrix linear control systems, we study the property of arbitrary matrix coefficient assignability for the characteristic matrix polynomial. This property is a generalization of the property of eigenvalue spectrum assignability or arbitrary coefficient assignability for the characteristic polynomial from system with scalar $(s=1)$ block matrices to systems with block matrices of higher dimensions $(s>1)$. Compared to the scalar case $(s=1)$, new features appear in the block cases of higher dimensions $(s>1)$ that are absent in the scalar case. New properties of arbitrary (upper triangular, lower triangular, diagonal) matrix coefficient assignability for the characteristic matrix polynomial are introduced. In the scalar case, all the described properties are equivalent to each other, but in block matrix cases of higher dimensions this is not the case. Implications between these properties are established.
Keywords: linear time-invariant control system, eigenvalue spectrum assignment, linear static feedback, block matrix system 
@article{VUU_2024_34_3_a2,
     author = {V. A. Zaitsev},
     title = {On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {339--358},
     year = {2024},
     volume = {34},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a2/}
}
TY  - JOUR
AU  - V. A. Zaitsev
TI  - On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2024
SP  - 339
EP  - 358
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a2/
LA  - en
ID  - VUU_2024_34_3_a2
ER  - 
%0 Journal Article
%A V. A. Zaitsev
%T On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2024
%P 339-358
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a2/
%G en
%F VUU_2024_34_3_a2
V. A. Zaitsev. On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 339-358. http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a2/

[1] Popov V.M., “Hyperstability and optimality of automatic systems with several control functions”, Revue Roumaine des Sciences Techniques. Série Électrotechnique et Énergétique, 9:4 (1964), 629–690 | MR

[2] Wonham W., “On pole assignment in multi-input controllable linear systems”, IEEE Transactions on Automatic Control, 12:6 (1967), 660–665 | DOI

[3] Brockett R., Byrnes C., “Multivariable Nyquist criteria, root loci, and pole placement: a geometric viewpoint”, IEEE Transactions on Automatic Control, 26:1 (1981), 271–284 | DOI | MR | Zbl

[4] Wang X., “Pole placement by static output feedback”, Journal of Mathematical Systems, Estimation, and Control, 2:2 (1992), 205–218 | MR

[5] Wang X., “Grassmannian, central projection, and output feedback pole assignment of linear systems”, IEEE Transactions on Automatic Control, 41:6 (1996), 786–794 | DOI | MR | Zbl

[6] Syrmos V.L., Abdallah C.T., Dorato P., Grigoriadis K., “Static output feedback — A survey”, Automatica, 33:2 (1997), 125–137 | DOI | MR | Zbl

[7] Sadabadi M.S., Peaucelle D., “From static output feedback to structured robust static output feedback: A survey”, Annual Reviews in Control, 42 (2016), 11–26 | DOI

[8] Shumafov M.M., “Stabilization of linear control systems and pole assignment problem: A survey”, Vestnik St. Petersburg University, Mathematics, 52:4 (2019), 349–367 | DOI | MR | Zbl

[9] Zaitsev V., Kim I., “Matrix eigenvalue spectrum assignment for linear control systems by static output feedback”, Linear Algebra and its Applications, 613 (2021), 115–150 | DOI | MR | Zbl

[10] Dennis Jr.J.E., Traub J.F., Weber R.P., “The algebraic theory of matrix polynomials”, SIAM Journal on Numerical Analysis, 13:6 (1976), 831–845 | DOI | MR | Zbl

[11] Dennis Jr.J.E., Traub J.F., Weber R.P., On the matrix polynomial, lambda-matrix and block eigenvalue problems, Technical Report No. 71–109 from Carnegie Mellon University Computer Science Department, Pittsburg, PA, 1971 | MR

[12] Gohberg I., Lancaster P., Rodman L., Matrix polynomials, SIAM, Philadelphia, 2009 | DOI | MR | Zbl