Design of proportional-plus-derivative output feedback for pole assignment

The paper studies the problem of pole assignment in linear multivariable systems using proportional-plus-derivative output feedback. A simple expression is obtained for the closed loop characteristic polynomial in terms of the unity-rank proportional and derivative feedback matrices. It is shown that when the system order does not exceed twice the number of inputs or outputs, all system poles can be assigned arbitrarily, and the required feedback matrices are obtained from linear equations. When the system order exceeds this value, the pole assignment problem becomes nonlinear and may be solved using the available numerical methods. Examples are given for illustration.