Eigenstructure assignment for stabilizable linear systems via state feedback

In this paper, a direct and explicit parametric solution of the matrix equation AV+BW=VF is proposed. Here [A B] is not required to be controllable. When [A B] is controllable, the solution obtained is a result previously obtained by Duan (1993). Based on the proposed solution of this matrix equation, a parametric approach for eigenstructure assignment in stabilizable linear systems via state feedback is established. The obtained result generalizes the approach proposed previously by Duan to the case with uncontrollable modes.