Stability analysis and robust control for uncertain nonlinear systems using singular perturbation method

Abstract

This dissertation presents the control design methods for the nonlinear systems containing the uncertainties. First, the robust stabilization of approximately feedback linearizable time-varying systems with uncertainties is considered. The original system is transformed into the singularly perturbed system by using high-gain feedback. Based on the Lyapunov stability theorem, a new stabilizing controller is proposed by using singular perturbation and feedback linearization. The proposed method relaxes the conditions for feedback linearization and compensates the effect of uncertainties. Second, the ultimate boundedness of the nonlinear singularly perturbed system with measurement noise is considered. In the nonlinear singularly perturbed system, the composite feedback controller is commonly used to stabilize the overall singularly perturbed system by using the slow subsystem and the fast subsystem. In the presence of the measurement noise, the composite feedback controller does not guarantee the ultimate boundedness of the singularly perturbed system with the measurement noise. Thus, we propose the modified composite controller to show the ultimate boundedness of the nonlinear singularly perturbed system with measurement noise. Third, the output feedback controller with fast state observer for the nonlinear singularly perturbed system is considered. We stabilize the nonlinear singularly perturbed system with the state feedback controller. The state feedback controller is suggested to stabilize the fast subsystem of the nonlinear singularly perturbed system. Then, by the stable slow manifold, the slow subsystem is stabilized. Using the state feedback controller and the fast state observer, we design the output feedback controller for the nonlinear singularly perturbed system. With the only fast state observer, we stabilize the nonlinear singularly perturbed system. Then, we consider the measurement noise in this system using proposed output feedback control ...