Robustness analysis of nonlinear systems with feedback linearizing control

The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performance of the feedback controller. This thesis introduces a design and analysis approach for robust feedback linearizing controllers for nonlinear systems. This approach takes into account these model errors and provides robustness margins to guarantee the stability of feedback linearized systems.Based on robust stability theory, two important tools, namely the small gain theorem and the gap metric, are used to derive and validate robustness and performance margins for the feedback linearized systems. It is shown that the small gain theorem can provide unsatisfactory results, since the stability conditions found using this approach require the nonlinear plant to be stable. However, the gap metric approach is shown to yield general stability conditions which can be applied to both stable and unstable plants. These conditions show that the stability of the linearized systems depends on how exact the inversion of the plant nonlinearity is, within the nonlinear part of the controller.Furthermore, this thesis introduces an improved robust feedback linearizing controller which can classify the system nonlinearity into stable and unstable components and preserve the stabilizing action of the inherently stabilizing nonlinearities in the plant, cancelling only the unstable nonlinear part of the plant. Using this controller, it is shown that system stability depends on the bound on the input nonlinear component of the plant and how exact the inversion of the unstable nonlinear of the plant is, within the nonlinear part of the controller.