Solving reduced biquaternion regulating equation based on semi-tensor product of matrices

Journal of Lanzhou University of Technology ›› 2023, Vol. 49 ›› Issue (1): 152-157.

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Solving reduced biquaternion regulating equation based on semi-tensor product of matrices

XI Yi-meng, LI Ying, LIU Zhi-hong, SUN Jian-hua

School of Mathematical Sciences, Liaocheng University, Liaocheng, 252000 China

Received:2022-03-03 Online:2023-02-28 Published:2023-03-21

Abstract

Abstract: Based on the semi-tensor product of matrices and the real vector representation of reduced biquaternion, the problem of reduced biquaternion regulating equations A₁X－A₂XB=C is transformed into a matrix equation on real number field without constraint, and then the (anti-)Hermitian solution of reduced biquaternion regulating equations is obtained by using real matrix equation. The effectiveness of this method is verified by numerical experiments. Finally, this method is applied to the continuous zeroing dynamics design of time-varying linear systems.

Key words: regulating equation, semi-tensor product of matrices, real vector representation, reduced biquaternion matrix

CLC Number:

O241.6

XI Yi-meng, LI Ying, LIU Zhi-hong, SUN Jian-hua. Solving reduced biquaternion regulating equation based on semi-tensor product of matrices[J]. Journal of Lanzhou University of Technology, 2023, 49(1): 152-157.

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Solving reduced biquaternion regulating equation based on semi-tensor product of matrices

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