| We study some global and semi-global control problems regarding two classes of systems, linear systems subject to input saturation and minimum-phase input-output linearizable systems. We organize the thesis into two parts, each of which deals with one of the two classes of systems.; The first part deals with linear systems subject to input saturation. Two design methodologies are developed to obtain the main results presented in the first part, as well as the second part of the thesis. More specifically, for both continuous-time and discrete-time systems, a low-gain state feedback design methodology yields both a family of linear state feedback laws and a family of linear dynamic output feedback laws which semi-globally exponentially stabilize the general asymptotically null controllable and detectable systems subject to input saturation. A low-and-high gain design methodology yields both a family of linear state feedback laws and a family of linear observer based output feedback laws that not only semi-globally asymptotically stabilizes a class of linear systems subject to input saturation, but also fully utilizes the control capacity and hence improves the closed-loop performances. The full utilization of the control capacity is also shown to achieve disturbance rejection.; The second part of the thesis deals with minimum-phase input-output linearizable systems. We first establish the global asymptotic stabilizability via adaptive high-gain output feedback under certain global growth conditions. The rest of this part of the thesis is devoted to the removing or relaxing of these global growth conditions. To this end, we start with the simpler case where an input-output linearizable system reduces to a partially linear composite system. Our results show that such a partially linear composite system is semi-globally asymptotically stabilizable by using linear or nonlinear feedbacks of only the linear subsystem state as long as the linear subsystem, adopting the part of state which enters the nonlinear subsystem as its output, is right invertible with all its invariant zeros located in the closed left half s-plane. We then return to the general input-output linearizable systems. For both the state feedback case and the output feedback case, we establish the semi-global asymptotic stabilizability and the semi-global practical stabilizability of such systems under some fairly weak conditions, most of which are necessary. |
