Open AccessDecoupling of cubic polynomial matrix systems
Author(s) -
Peizhao Yu,
Guoshan Zhang,
Yi Zhang
Publication year - 2021
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2020012
Subject(s) - polynomial matrix , matrix polynomial , invertible matrix , isospectral , mathematics , decoupling (probability) , cubic function , matrix (chemical analysis) , cubic form , polynomial , characteristic polynomial , diagonal matrix , pure mathematics , mathematical analysis , diagonal , geometry , materials science , control engineering , engineering , composite material
The decoupling of polynomial matrix system is to diagonalize its system matrix. In this paper, decoupling problems for cubic polynomial matrix system are considered. The decoupling conditions for a class of cubic polynomial matrix systems are derived under strict equivalence transformation. By using linearization, isospectral decoupling method for cubic polynomial matrix system is proposed. To be specific, necessary and sufficient conditions of isospectral diagonalization for nonsingular cubic polynomial matrix are given. These results are extended to singular cubic polynomial matrix. Solving processes are given to obtain isospectral diagonal cubic polynomial matrix for nonsingular and singular cases. Finally, illustrating examples are provided to verify the main results.