Observers and Controllers for Feedback Linearizable Systems

If the states are available through measurments, both theories and applications indicate that feedback linearizable systems can be controled using the feedback tansformation and linear design methods. However, there is no general theory regarding performance if estimated states instead of actual states are used in the feedback process. For feedback linearizable systems we construct a nonlinear observer which performs well in state feedback for asymptotically stabilizing controls and for nonlinear steady state analysis. The results of this paper rest on the fact that for our nonlinear observer, every nonlinear term in the overall system (the original system after feedback plus the error equation for the observer) depends on the difference between states and their estimates in canonical coordinates. This phenomenon seems to be unique to feedback linearizable systems.