This dissertation presents a series of progress in the synthesis of nonlinear systems, including global adaptive stabilization by output feedback, global servomechanism by error feedback, observer design for feedback linearizable nonlinear systems and global stabilization by output feedback for inherently nonlinear systems.
The problem of global stabilization by output feedback for a class of uncertain nonlinear systems with unknown growth rates is first studied in this dissertation. An output feedback controller is generally hard to be designed for these nonlinear systems, since some design parameters in the controller are usually related to the unknown growth rates. Using the ideas coming from universal control, an universal adaptive output feedback controller can be explicitly constructed, such that all the states of uncertain nonlinear systems can be regulated to zero.
It is known in the control literature that the global servomechanism problem can be transformed into the global stabilization problem by introducing the internal model and the proper change of coordinates. Therefore, the advance in global stabilization can be further employed to solve the global servomechanism problem.
A traditional high-gain observer is usually constructed for a nonlinear system to recover unmeasurable states, if the system satisfies the global Lipschitz condition. However, generally speaking, the global Lipschitz assumption is somewhat too strong to be satisfied for nonlinear systems. Therefore, a new observer design is presented for the autonomous observable nonlinear systems under the bounded trajectory condition. Since the bound of the solution trajectory depends on the initial condition and is therefore not known, the traditional high gain observer can not be applied under this case. In the new observer design, this difficulty can be overcome by combining the idea of universal control to tune the observer gains on line.
To globally stabilize nonlinear systems by output feedback, it is known that suitable growth conditions should be imposed on the nonlinearities, since some nonlinear systems have the unboundedness observability property. In most cases, the nonlinearities are required to be only linear growth with respect to the unmeasurable states. In the last two parts of this dissertation, it is indicated that the linear growth condition can be further relaxed. The new growth condition can encompass most existing conditions and provides a unified framework for studying global stabilization of nonlinear system by output feedback.