Optimality in the eigenvalue assignment problem

The authors study the eigenvalue assignment problem, which involves finding a state feedback vector k such that the eigenvalues of A-bk/sup T/ are in the desired locations in the case where the system is not completely controllable, and the solution for the feedback gain vector k is not unique. The set of possible solutions for the feedback gain vector is identified, and optimal solutions are defined in the sense of minimum two-norm, minimum infinite-norm (minimum maximum gain), and maximum number of zero gain elements in k. The methods can also be applied to the case where linear state-variable feedback is applied to more than one input.<>