On solutions of the con-Yakubovich matrix equation X − AX̅F = BY

The con-Yakubovich matrix equation X - AX̅F = BY is investigated in this paper. An explicit general solution of this equation is given by a finite sum. In addition, the solution can be equivalently expressed in terms of con-controllability and con-observability. Another feature of the obtained solution is that the matrix F explicitly appears in the expression, which allows the matrix F to be undetermined. Finally, a numerical example is employed to show the effectiveness of the proposed approach.