Direct Gradient Descent Control as a Dynamic Feedback Control for Linear System

In this paper we study about stabilization of linear control system by using the dynamic state/output feedback control. We can prove that the dynamic state feedback control exists if the static state feedback control exists. But the existence of the dynamic output feedback control can not be guaranteed only by the existence of static feedback control, passive condition is needed. By applying the direct gradient descent control as a dynamic state feedback control to linear system, we get a condition for guaranteing the asymptotic stability of the system.