Abstract
The current study investigates the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix equations. Accordingly, the necessary and sufficient conditions for the consistency of these systems are determined, and the general solutions of the systems are thereby deduced. An algorithm and a numerical example are constructed over the quaternions to validate the results of this paper.
Highlights
Sylvester-like matrix equations and their generalizations have applications in many scientific fields such as graph theory [1], image processing [2], output feedback control [3], neural networks [4], eigenvalue assignment problems [5], robust control [6] and so on
The iterative methods of solving linear and nonlinear Sylvesterlike matrix equations are built on numerical solution methods [18–27]
Lee and Vu [29] conducted a thorough examination of the general solution and solvability conditions for the following coupled system of matrix equations: A1X + YB1 = C1, (5)
Summary
Sylvester-like matrix equations and their generalizations have applications in many scientific fields such as graph theory [1], image processing [2], output feedback control [3], neural networks [4], eigenvalue assignment problems [5], robust control [6] and so on (for example, see [7–17]). In [30,33], He and Wang presented the solvability conditions and the general solution for the following Sylvester-like matrix equation: A1X1 + X2B1 + C3X3D3 + C4X4D4 = E1. They presented these findings in terms of the Moore–Penrose inverse of certain given matrices. The resulting equation has wide applications in the linear matrix equations field, see [7,34–40] He and Meng [41] derived the rank equalities solvability conditions for the following quaternion matrix equation with two different restrictions: A1Z1B1 + A2Z2B2 + A3Z3B3 = C1, DZ1 = F, Z1 H = G.
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