A system of quaternary coupled Sylvester-type real quaternion matrix equations

Solutions to the linear transpose matrix equations and their application in control

“…In the present work, we are not concerned the numerical solutions to the linear transpose matrix equations and we suggested the readers to see (Zhou et al 2011;Wang et al 2007;Xie et al 2010) and their references therein. Besides the topics above on linear matrix equation, some other topics were also focused on: for instance, the solutions to the (generalized) Sylvester matrix equation over real field, complex field and quaternion field; for details, please see (Jiang and Wei 2003;He et al 2018;He 2014, 2013;Duan 2005, 2006;Wu et al 2009;He et al 2020He et al , 2017Wang et al 2011;Wang and Li 2009;Ma 1966). Here we should be pointed out that one of the important remarkable results is the solutions to the Sylvester matrix equation over complex or quaternion field Duan 2005, 2006;He et al 2020He et al , 2017Wang et al 2011;Wang and Li 2009;Wang and Zhang 2008).…”

Distributed optimisation design for solving the Stein equation with constraints

“…In fact, researchers have been paying lots of attention to solving the Stein equation itself and variants as well as their properties for decades (e.g. see [14, 18, 19]), and proposed quite a few algorithms from different perspectives. The existing direct methods include a Schur‐form type method for small size coefficient matrices proposed in [20] and a generalisation of the Hammarling method proposed in [21].…”

Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation

“…Systems of periodic discrete-time coupled Sylvester quaternion matrix equations [10], systems of quaternary coupled Sylvester-type real quaternion matrix equations [11], and optimal pole assignment of linear systems by the Sylvester matrix equations [12] have been explored. Some constraint generalized Sylvester matrix equations [13,14] were studied recently.…”