Stabilization of uncertain equilibrium points by dynamic state-derivative feedback control

We consider a local stabilization problem of an uncertain equilibrium point existed in a nonlinear continuous-time system by a state-derivative feedback controller. In previous researches, it is investigated that the uncertainty of the equilibrium point results in nonzero steady-state control input so that a different equilibrium point is stabilized. Then, a feedback controllers with steady-state blocking zeros eliminate the dependence on the steady-state. In this paper, we focus on the class of state-derivative feedback control, and develop a design method for a dynamic state-derivative feedback controller with steady-state blocking zeros. The proposed controller can reject the dependence on the uncertainty of equilibrium points. Moreover, we illustrate the effectiveness of the proposed control method by the numerical example which is the stabilization problem of the uncertain equilibrium point. In addition, we show that the poles of the closed-loop system with the proposed dynamic controller can be assigned at the desired locations.