Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

摘要

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearizing controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearizing control schemes by introducing a more general robust feedback linearizing control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilizing action of the inherently stabilizing nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities andthe accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.