This thesis is concerned with problems in nonlinear H_∞(L₂) control theory and its applications.

The first part of this thesis develops a solution to the H_∞(L₂) control problem, by output feedback, for nonlinear plants with general input affine structure. Nonlinear input affine systems have been shown to approximate a large class of physical systems. Unlike previous approaches to this problem, the procedure developed here is not restricted by structural simplifications on the plant model.

The second part of this thesis uses the results on H_∞(L₂) control developed in the first part to approach nonlinear robust stabilization problems. Several types of unstructured plant uncertainty problems are solved by embedding each problem in a generic robust stabilization problem with feedback uncertainty.

The third part of the thesis uses these developments to treat the problem of nonlinear controller order reduction by H_∞ balancing. Conditions are derived which ensure that the reduced order controller stabilizes not only the reduced order plant but also the full order plant. This is done by relating the order reduction problem to a robust stabilization problem.

The last part of the thesis is concerned with developing results on the parameterization of classes of nonlinear H_∞(L₂) controllers. The nonlinear H_∞(L₂) control problem is reformulated in terms of the chain representation of a given plant. A procedure is developed for constructing a class of controllers which solve the H_∞(L₂) control problem locally. This procedure involves the state space characterization of J-dissipative (J-lossless) systems together with two types of coprime factorizations. The problems considered correspond to the general two block and four block problems in linear H_∞ control theory.