Constrained two-sided coupled Sylvester-type quaternion matrix equations

Wang, Qingwen; He, Zhuo-Heng; Zhang, Yang

doi:10.1016/j.automatica.2018.12.001

Cited by 56 publications

(21 citation statements)

References 25 publications

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“…All the rank equalities in (18)- (20) hold. Hence, the real quaternion matrix equation 17has a φ-Hermitian solution (X, Y, Z).…”

Section: Solvability Conditions and General φ-Hermitian Solution To (2)mentioning

confidence: 99%

“…Quaternion matrix equation and its general Hermitian solutions play important roles in dealing with many problems arising from systems and control theory [14]. There have been many papers using different approaches to investigate the real quaternion matrix equations (e.g., [1]- [5], [11]- [13], [15], [16], [20], [21]). For instance, Rodman [14] gave a necessary and sufficient condition for the existence of a unique solution to the Sylvester quaternion matrix equation.…”

Section: Introductionmentioning

confidence: 99%

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Some quaternion matrix equations involving Φ-Hermicity

2019

Filomat

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Let H be the real quaternion algebra and H m×n denote the set of all m × n matrices over H. For A ∈ H m×n , we denote by A φ the n × m matrix obtained by applying φ entrywise to the transposed matrix A t , where φ is a nonstandard involution of H. A ∈ H n×n is said to be φ-Hermitian if A = A φ. In this paper, we construct a simultaneous decomposition of four real quaternion matrices with the same row number (A, B, C, D), where A is φ-Hermitian, and B, C, D are general matrices. Using this simultaneous matrix decomposition, we derive necessary and sufficient conditions for the existence of a solution to some real quaternion matrix equations involving φ-Hermicity in terms of ranks of the given real quaternion matrices. We also present the general solutions to these real quaternion matrix equations when they are solvable. Finally some numerical examples are presented to illustrate the results of this paper.

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“…All the rank equalities in (18)- (20) hold. Hence, the real quaternion matrix equation 17has a φ-Hermitian solution (X, Y, Z).…”

Section: Solvability Conditions and General φ-Hermitian Solution To (2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some quaternion matrix equations involving Φ-Hermicity

2019

Filomat

Self Cite

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“…As one of the fundamental mathematical problems, Sylvester matrix equation is widely encountered in scientific and engineering fields [1,2,3,4,5], the general form of which is formulated as…”

Section: Introductionmentioning

confidence: 99%

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

Shi

Jin

et al. 2020

Journal of the Franklin Institute

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“…In the past few years, several types of matrix equations over some quaternion algebras have been studied by using the real/complex representation method and some other techniques (see, e.g., other studies [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] ). For instance, using the particular structure of the real/complex representations of quaternion matrices as well as the Kronecker product of matrices, Zhang et al 26 and Yuan et al 27 derived several kinds of solutions to the split quaternion matrix equation AXB + CXD = E, respectively.…”

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confidence: 99%

The generalized quaternion matrix equation AXB+CX^⋆D=E

Liu

Zhang

2020

Math Methods in App Sciences

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In this paper, we discuss the generalized quaternion matrix equation AXB+CX⋆D=E, where X⋆ is one of X, X*, the η‐conjugate or the η‐conjugate transpose of X with η∈{i,j,k}. Two new real representations of a generalized quaternion matrix are proposed. By using this method, the criteria for the existence and uniqueness of solutions to the mentioned matrix equation as well as the existence of X=± X⋆ solutions to the generalized quaternion matrix equation AXB+CXD=E are derived in a unified way.

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Constrained two-sided coupled Sylvester-type quaternion matrix equations

Cited by 56 publications

References 25 publications

Some quaternion matrix equations involving Φ-Hermicity

Some quaternion matrix equations involving Φ-Hermicity

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

The generalized quaternion matrix equation AXB+CX^⋆D=E

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Constrained two-sided coupled Sylvester-type quaternion matrix equations

Cited by 56 publications

References 25 publications

Some quaternion matrix equations involving Φ-Hermicity

Some quaternion matrix equations involving Φ-Hermicity

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

The generalized quaternion matrix equation AXB+CX⋆D=E

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Product

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The generalized quaternion matrix equation AXB+CX^⋆D=E