(A) study on global stabilization of non-homogeneous high-order systems via output feedback control

Abstract

In this thesis, we investigate non-homogeneous high-order systems whose linearization at origin is uncontrollable and unobservable. The non-homogeneous high-order system is high-order system with non-homogeneous nonlinear term. In particular, we study global stabilization of non-homogeneous high-order system via output feedback control. We present that global stabilization of non-homogeneous high-order systems is possible via state feedback control which is analyzed by adding a power integrator technique. For the non-homogeneous high-order system with known non-homogeneous terms, we propose design of a reduced-order nonlinear observer and procedure to select observer gains step by step. We present that the non-homogeneous high-order system with known non-homogeneous terms is globally asymptotically stable via output feedback control. The existence of uncertainty degrades the control performance and makes sometimes the system stabilizing difficult. Therefore, we consider non-homogeneous high-order system with uncertain non-homogeneous terms. We suggest design of a reduced-order nonlinear observer and procedure to select observer gains recursively. We propose that the non-homogeneous high-order system with uncertain non-homogeneous terms is globally asymptotically stable via output feedback control. We regard the non-homogeneous systems as given systems and analyze stability of them. However, we need to check whether any general nonlinear systems can be transformed into the high-order system or non-homogeneous high-order system. Therefore, we investigate transformation of the general nonlinear systems into them. We propose that the general nonlinear systems are able to be transformed into them by diffeomorphism. Also, we propose that the general nonlinear systems are globally asymptotically stable via output feedback control which is designed and analyzed in the transformed systems.