Algorithm for decoupling and complete pole assignment of linear multivariable systems

The problem of decoupling and complete pole assignment of linear square, and controllable systems by static state feedback is addressed in this paper. Based on a characterization of the whole set of attainable finite pole-zero structures of a decouplable system, we present a reliable numerical algorithm which tests the conditions for decoupling and computes the state feedback which decouples the system with a particular pole-zero finite structure, avoiding unnecessary cancellations of invariant zeros. With the use of this algorithm, fixed decoupling poles are determined, non-fixed poles can be arbitrarily located, and no cancellation of system invariant zeros is produced if this is not necessary for decoupling.