Controller design for global stability of approximate feedback linearizable nonlinear systems with uncertainty

Abstract

Even though many practical systems have nonlinear structure, there is no general method to control nonlinear systems. For last two decades, approximate feedback linearization has received attention in nonlinear control field. If the approximate feedback linearization can be applied to a nonlinear system, the nonlinear system is transformed into a chain of integrators with a perturbed term called perturbed chain of integrators system. Many control methods have been studied to stabilize the perturbed chain of integrators system under some assumptions in which the perturbed term satisfies feedforward condition or triangular condition. However, the previous control methods cannot guarantee their stability performance when the perturbed term does not satisfy either the feedforward condition or the triangular condition. In this thesis, we consider more generalized condition in which some parts of the perturbed term satisfy the feedforward condition, and the other parts of the perturbed term satisfy the triangular condition. Moreover, the condition also covers the case that all parts of the perturbed term satisfy either the feedforward condition or the triangular condition. Under the condition, we propose a state feedback control method to globally exponentially stabilize the perturbed chain of integrators system, and then we extend the state feedback control method to output feedback control method. When we show Lyapunov stability, we utilize some concepts of the singularly perturbed system analysis framework. We also show that the control method can be available in lack of information about the linear growth rate of the condition. In addition, when some parts of control gains have extremely high or low value, we present a gain tuning method to relax the extreme parts.