Output feedback control of nonlinear systems with unstabilizable/undetectable linearization

This dissertation addresses a number of fundamental and challenging output feedback control problems for a significant class of uncertain nonlinear systems with unstabilizable/undetectable linearization including: (1) global asymptotic stabilization via smooth output feedback under a high-order version of Lipschitz-like condition; (2) robust control by smooth or nonsmooth output feedback with dynamic rescaling, under appropriate yet restrictive growth conditions; (3) semi-global asymptotic stabilization of non-uniformly observable and nonsmoothly stabilizable systems by nonsmooth output feedback, without imposing any growth condition.; First of all, we study the problem of global stabilization by smooth output feedback, for a class of n-dimensional systems whose Jacobian linearization is neither stabilizable nor detectable. A novel output feedback control scheme is proposed for the explicit design of both high-order observers and controllers in a recursive manner. Its design philosophy is substantially different from that of the traditional "Luenberger" observer in which the observer gain is determined by observability.; Using the new output feedback design method, we then consider the problem of robust smooth or nonsmooth output feedback stabilization for several families of uncertain nonlinear systems with unstabilizable/undetectable linearization. To handle system uncertainties effectively, we introduce a novel rescaling transformation with an appropriate dilation and factor. Depending on the type of growth conditions, the rescaling factor can be either a sufficiently large constant or a time-varying function that needs to be tuned on-line through a Riccati-like differential equation. The constructions of smooth or nonsmooth state feedback controllers and observers use only the knowledge of the bounding system rather than the uncertain system itself. The robust output feedback design approach thus developed is also extended to uncertain cascade systems beyond a strict-triangular structure.; In the last part of this thesis, we show that without imposing any growth condition, semi-global stabilization by nonsmooth output feedback can be achieved for a chain of odd power integrators perturbed by a triangular vector field, which is in general not smoothly stabilizable nor uniformly observable.