Stabilization of multivariable linear time-invariant systems by proportional-plus-derivative state feedback

This paper is devoted to the study of the problem of stabilization by proportional-plus-derivative state feedback for multivariable linear time-invariant systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system obtained by proportional-plus-derivative state feedback from the given multivariable linear time-invariant system. A procedure is given for the computation of stabilizing proportional-plus-derivative state feedback. Our approach is based on properties of real and polynomial matrices.