Stabilizing control design of fully linearizable systems via estimated states

This paper is concerned with the problem of designing stabilizing controllers for nonlinear systems using feedback linearization with estimated states. It is assumed that the systems under consideration are fully linearizable, but the full state is not completely accessible, so that an observer is included in the loop. Sufficient conditions are set to guarantee that the overall system trajectories asymptotically converge to those obtained with feedback linearization using the true states, so that a stabilizing control law can be established. Our results are applied to the stabilizing control design for a model of an experimental prototype of magnetic levitation system, assuming that only the state representing object position is measured at the output, and thus, not assuming that the full state is measured. The behaviour of our control scheme is illustrated by simulation results.