This dissertation presents a discussion of the optimal feedback control for nonliner systems (both discrete and ODE) and nonquadratic cost functions in order to achieve improved performance and larger regions of asymptotic stability in the nonlinear system context. The main work of this thesis is carried out in two parts; the first involves development of nonlinear, nonquadratic theory for nonlinear recursion equations and formulation, proof and application of the stable manifold theorem as it is required in this context in order to obtain the form of the optimal control law. The second principal part of the dissertation is the development of nonlinear, nonquadratic theory as it relates to nonautonomous systems of a particular type; specifically periodic time varying systems with a fixed, time invariant critical point. / Ph. D.