Robust Derivative Feedback Control for Systems with Uncertain Equilibrium States

This paper investigates the robust stabilization of nonlinear dynamic systems with uncertain or unknown equilibrium states by derivative feedback control. A generalized design method for the state-derivative feedback controller is presented to stabilize the dynamics of nonlinear systems at their true equilibrium state, when the exact location of such equilibrium is unknown in the design and implementation of the feedback control law. The robustness of the derivative feedback controller to norm-bounded dynamic model uncertainty is also investigated, and linear matrix inequality conditions are derived to guarantee the stability of the closed-loop system. The proposed control scheme is tested on the Rossler attractor, which exhibits complex chaotic behavior when uncontrolled, and we demonstrate the effectiveness of our derivative feedback solution.