Bounded Derivative Feedback Control with Application to Magnetic Levitation

Abstract In this paper, we study the stabilization of dynamic systems with uncertain equilibrium states and in the presence of bounded control. We propose state and output derivative feedback control schemes to stabilize the dynamic system, and to drive the system states to its true equilibrium state even when the location of such equilibrium is uncertain. Control bounds in the feedback control are also considered in this paper, and stability conditions are derived for the cases when the control energy is bounded, and when the maximum control is bounded. Stability conditions are derived in the form of matrix inequalities for both cases of control bounds, and numerical methods are discussed to synthesize feasible control solutions. The effectiveness of the proposed method is illustrated by an experimental implementation.