Output feedback control for nonlinear systems using variable structure control

We study stabilization and output tracking for feedback linearizable systems using output feedback variable structure control in the presence of modeling error and/or external disturbance. In particular, a stabilization problem is studied for a nonlinear system that can be transformed into a normal form with no zero dynamics. A tracking problem is studied for a nonlinear system that is represented by an input-output model, which can be transformed into the normal form with asymptotically stable zero dynamics. In both cases a robust high-gain observer is used to estimate the state variables while rejecting disturbances. A globally bounded discontinuous variable structure controller is designed to compensate for modeling error and/or external disturbance. For the stabilization problem, we show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon which exists in previous designs. In the tracking problem, we show that the controller ensures tracking of the reference signal in the presence of unknown time-varying disturbances and modeling errors. We give regional as well as semiglobal results, but we do not require exponential stability of the zero dynamics nor global growth conditions. As an application, we design a controller, with only position measurement, that ensures tracking of a desired path for an n degree of freedom robot manipulator. A high-gain observer is used to estimate the angular velocities.