Pole assignment for three-dimensional systems using two-dimensional dynamic compensators

The author studies the pole assignment problem for 3D systems. The denominator of the transfer functions of the closed-loop system is transformed into the product of three stable 1D polynomials by performing 2D dynamical feedback and input transformation on the given 3D systems. The author then considers the possibility that these 2D dynamic compensators are realizable, and proposes a countermeasure in case they are not realizable. He also obtains the conditions of the stability of the closed-loop 3D systems. He calculates the dynamical dimension which is necessary for the pole assignment, and proposes the pole assignment method with the lowest dynamical dimension