Globally stabilizing output feedback methods for nonlinear systems

The non-local stabilization of nonlinear systems by output feedback is a challenging problem that remains the subject of continuing investigation in control theory. In this thesis we develop two globally asymptotically stabilizing output feedback algorithms for multivariable nonlinear systems. Our first result is an extension of the output feedback method presented in [2] to a class of nonlinear systems whose dynamics can be written as a collection of subsystems that are dynamically coupled through output-dependent nonlinear terms. We show that the method given in [2] must be modified to accommodate this dynamic coupling by introducing additional nonlinear damping terms into each control input. Our second contribution involves the application of observer backstepping to systems in a restricted block-triangular observer form. In this form, the nonlinearities entering each subsystem are allowed to depend on the output associated with the subsystem, and all upper subsystem states, including unmeasured ones. The proposed algorithm is demonstrated on a magnetically levitated ball.