Generalized pole placement via static output feedback: A methodology based on projections

This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given n subsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed-loop system. The algorithm presented is iterative in nature and is based on alternating projection ideas. Each iteration of the algorithm involves a Schur matrix decomposition, a standard least-squares problem and a combinatorial least-squares problem. While the algorithm is not guaranteed to always find a solution, computational results are presented demonstrating the effectiveness of the algorithm.