Stabilization of Single-Input LTI Systems by Proportional-Derivative Feedback

This article presents an efficient solution to the stabilization pole placement problem for single-input linear time-invariant (LTI) systems by proportional-derivative (PD) feedback. For a controllable system, any arbitrary closed-loop poles can be placed in order to achieve the desired closed-loop system performance. Its derivation is based on the transformation of linear system into Hessenberg form by a special coordinate transformation before solving the pole placement problem. The available degrees of freedom offered by PD feedback are utilized to obtain closed-loop systems with small gains. So, the minimization problem for a suitably chosen cost function is formulated. Simulation results are included to show the effectiveness of the proposed approach.