| The notion of controlling and manipulating nonlinear dynamic systems has been pursued by numerous researchers over the past century, with the majority of the research beginning in the early 1980's, with various goals and conditions imposed on systems dynamics, descriptions, etc. This dissertation is a collection of works dedicated to further the theory behind such an endeavor, with the primary accomplishments revolving around stabilizing highly nonlinear systems in the face of uncertain system knowledge and limited measurements. These restrictions force the use of robust techniques and the estimation of unmeasurable state dynamics.; First, we describe in detail a method to stabilize inherently nonlinear systems by full state feedback in a robust manner such that only the bounding functions of the nonlinear perturbations must be known. This procedure has a novel feature in that it contains several other existing design schemes as special cases. Also, where the most general of the design schemes were limited to non-smooth control law creations for all cases, this new method lifts that restriction in cases where a smooth control law may exist. This method can be considered a generalization, and hence unification, of the previously existing methods.; Second, this dissertation then focuses on the output feedback problem and addresses some current deficiencies in the existing literature, namely the inclusion of fast-growing nonlinearities in the system dynamics. This issue is addressed for a variety of problem settings, such as inherently nonlinear systems, large-scale systems, and systems with both slow-growing and fast-growing nonlinearities. We also look at feedforward systems and using nested saturations for output feedback control.; These schemes, systematic in nature, generalize the current state of nonlinear control theory and lift some restrictive conditions, which largely extends the class of systems that can now be robustly stabilized. |
