On the existence of solutions of the linear matrix equation XF−Y=0 with the rank constraint

In this paper, we present some sufficient conditions for the existence of solutions of the constrained linear matrix equation, which play an important role in designing and analyzing a direct parametric control approach for the eigenstructure assignment problem. Based on these sufficient conditions, the solution of this constrained linear matrix equation is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the proposed algorithm.