A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
Many problems in systems and control theory require the solution of Sylvester's equation \(AX-YB=C\) or of its generalization \((*)\) \(AXB+CYD=E\). The author studies the couple of matrix equations \((**)\) \(A_1XB_1=C_1,A_2XB_2=C_2\) over an arbitrary regular ring with identity. He obtains necessary and sufficient conditions for the consistency of the system \((**)\) and presents its general solution. The results are used to obtain necessary and sufficient conditions for the consistency of the equation \((*)\) and to derive the form of its general solution.
scientific article; zbMATH DE number 2083491