Design of Pole Assignment using m-Order Compensators

In this paper, we present some results of pole assignment by using m-order compensators in single-loop configurations with transfer function approach. The results are tightly related to the property of observability indices of the plant. In particular, we shall prove that by using m-order output feedback compensators, m+Em closed-loop poles can be almost arbitrarily assigned, where Em is determined by m and the observability indices of the plant. A complete parametrization for the characteristic polynomial of the feedback system in the multi-input multi-output case will be indicated, which can be used to assign more poles. The proofs of the results are the constructive design procedures. An example will be shown to illustrate the design.