A Constraint System of Generalized Sylvester Quaternion Matrix Equations

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

“…(v) Finally, for the second term Y 2 = P 푆 B † CM * , † = ( (2) 푝푔 ) of (44) using (14) for a determinantal representation of P 푆 , and due to Theorem 10 for B † CM * , † , we obtain…”

“…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.…”

Cramer’s rules for the system of quaternion matrix equations withη-Hermicity

“…An iterative algorithm for determining g (-skew)-Hermitian least-squares solutions to the quaternion matrix equation 3was established in [27]. For more related papers on g-Hermicity and its generalization, /-Hermicity, one may refer to [28][29][30][31][32][33][34][35][36][37][38].…”

The General Solution of Quaternion Matrix Equation Having η‐Skew‐Hermicity and Its Cramer’s Rule

“…bearing -Hermicity over H. An iterative algorithm for determining the -Hermitian and -skew-Hermitian solutions to the quaternion generalized Sylvester equation + = were established in [22]. For more related papers on -Hermicity, one may refer to [23][24][25][26][27][28]. Notice that Sylvestertype matrix equations have a huge amount of practical applications in feedback control [29,30], robust control [31], pole/eigenstructure assignment design [32], neural network [33], and so on.…”