Robust stabilization at uncertain equilibrium by output derivative feedback control

The problem of stabilizing dynamic systems with unknown or uncertain equilibrium states is studied. Derivative control schemes are proposed for both state and output feedback for the local stabilization at the true equilibrium states. The case where norm-bounded uncertainties are present in the system model is considered to derive robust stability conditions in linear matrix inequality form. The proposed control solutions drive the closed-loop system exponentially to its equilibrium states as shown via simulation on the chaotic Rössler and Lorenz attractors, when the equilibrium states are unknown and model uncertainties are present. A practical example involving a magnetic levitation system, in which two disks are to be levitated at an unknown magnetic equilibrium, demonstrates the effectiveness of the output derivative feedback controller.