Robustness Analysis of Feedback Linearisation for Uncertain Rational Systems

Feedback Linearisation (FL) is a nonlinear control technique that has gained a lot of attention in the past 30 years. Due to its relatively simple synthesis, the use of FL has been investigated particularly in the aerospace community, because aircraft models are often highly nonlinear and a controller is needed that can guarantee good performance over a wide range of operating conditions. However, mathematical models of real-life physical systems always have a level of uncertainty on them, as they are only ever approximations to the real system. In the current literature, the robustness of FL control has been analysed by extensive simulations, which may miss some worst-case combinations of uncertainties in the model. Alternatively, the robustness of the controlled system has been analysed on simplified linear models, using techniques from classical control, which do not well represent the inherently nonlinear dynamics of the system. This thesis contributes to the literature by using more recent techniques for analysis of nonlinear systems to assess robust stability under FL control. We apply advanced robust and nonlinear analysis techniques without the assumption that the controller has direct access to all the states of the system, by including state estimation or sensors in the closed loop for analysis. We also develop an existing analysis technique in the literature to show that a system under approximate FL control does not violate position limits of the actuator, despite uncertainty in the model, improving the rigour of the analysis. This is applied to a high-fidelity model of an aircraft, designed for use in industry and academia.