Further Results on the Differential Geometric Approach to Nonlinear Systems Affine in Control

The dissertation focuses on the differential geometric approach to nonlinear systems affine in control. Constructive algorithms are proposed for the structural decomposition of nonlinear systems to reveal the structural properties and to represent them in various normal forms. By exploiting these structural properties, the problems of global stabilization, semi-global stabilization, disturbance attenuation and almost disturbance decoupling are revisited.;The dissertation first deals with the structural decomposition of a nonlinear system. We propose constructive algorithms for decomposing nonlinear systems that are affine in control but otherwise general. These algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs. They lead to various normal form representations of a nonlinear system and reveal its structure at infinity, its zero dynamics and its invertibility properties, all of which represent nonlinear extensions of relevant linear system structural properties.;We exploit the properties of such a decomposition in solving the stabilization problem. In particular, this structural decomposition simplifies the conventional backstepping design and motivates new backstepping design procedures that are able to stabilize some systems on which the conventional backstepping is not applicable.;We further exploit the properties of such a decomposition in solving the semi-global stabilization problem for minimum phase nonlinear systems without vector relative degrees. By taking advantage of special structure of the decomposed system, we first apply the low gain design to the part of system that possesses a linear dynamics. The low gain design results in an augmented zero dynamics that is locally stable at the origin with a domain of attraction that can be made arbitrarily large by lowering the gain. With this augmented zero dynamics, the backstepping design procedure is then applied to achieve semi-global stabilization of the overall system.;We finally address the problems of disturbance attenuation and almost disturbance decoupling. By employing the structural decomposition of nonlinear systems and the new backstepping procedures that were developed, we show that these two problems can be solved for a larger class of nonlinear systems.