A computational algorithm for pole assignment of linear single-input systems

An efficient computational solution of the pole assignment problem of linear single-input systems is presented. It is based on orthogonal reduction of the closed-loop system matrix to upper (quasi-) triangular form whose 1 × 1 or 2 × 2 diagonal blocks correspond to the desired poles. The algorithm proposed is numerically stable and performs equally well with real and complex, distinct, and multiple desired poles. The number of the computational operations is less than6n^{3}, the necessary array storage being2n^{2} + 6nworking precision words, wherenis the order of the system.