An algorithm for the multiinput eigenvalue assignment problem

A very simple and inexpensive algorithm is presented for pole placement in the multiinput case. The algorithm consists of orthogonal reduction to a Block-Hessenberg form and a simple linear recursion. It yields a matrix F such that A+BF has any specified set of eigenvalues whenever the system is controllable. It is extremely easy to program on a computer. The algorithm is not a robust pole-placement algorithm but appears to give comparable results in most well-conditioned cases at a fraction of the cost. It is a direct (noniterative) algorithm and no eigenvalues or singular values are computed. The algorithm does not need any complex arithmetic, even when complex conjugate eigenvalues need to be assigned