Derivative feedback control of nonlinear systems with uncertain equilibrium states and actuator constraints

In this paper, we study the local stabilization of nonlinear systems with uncertain equilibrium states and in the presence of actuator constraints. We propose a derivative feedback control scheme to stabilize the nonlinear system, and to drive the system states to its true equilibrium state even when the location of such equilibrium is uncertain. Actuator constraints in the feedback control are also considered in this paper, and stability conditions are derived for the cases when the actuator output energy is bounded, and the actuator output is subject to saturation. Stability conditions are derived in the form of matrix inequalities for both cases of actuator constraints, and numerical methods are discussed to synthesize feasible control solutions. The effectiveness of the proposed method is illustrated by a numerical example, and experimentally demonstrated through a magnetic levitation test rig.