Robust stability analysis and controller synthesis for systems with parametric uncertainties

This dissertation covers our study of both robust stability analysis and robust controller synthesis for systems with highly structured uncertainties. These problems have attracted much interest in advanced control engineering, but experienced limited development in the past two decades. In 1997, an important observation was introduced with the critical direction theory (CDT). According to the theory, on the Nyquist plane at any given frequency, only the uncertain plants located along a specified direction, namely the critical direction, are of relevance to the stability analysis; all other uncertain plants that do not lie in the critical direction can be ignored when dealing with stability analysis. This dissertation extended the theory to systems with highly structured uncertainties, and explored the CDT's advantages over other approaches.;Firstly, robust stability analysis was addressed in this dissertation for systems with real-valued uncertainties. For SISO systems with affine real-valued uncertainties, we transformed the problem into a linear feasibility (LF) problem, together with an algorithm for calculating the parametric stability margin that was defined as the maximum scaling value of the uncertainties in maintaining the robust stability of the system. This algorithm used a bisection algorithm to achieve computational efficiency. Then we developed a linear programming (LP) and an iterative algorithm based on CDT for the same problem. All the three algorithms produced the same results for the examples simulated in this dissertation. Finally we related the parametric stability margin with the real mu results reported recently in the literature, and found consistency in using the critical direction theory and mu analysis. Our research on robust analysis provided an alternative real-mu analysis with clear geometrical explanation. Furthermore, our research on robust analysis establishes a sound foundation for robust synthesis research reported as follows.;Then, we addressed robust controller synthesis for systems with highly structured uncertainties. We constructed a systematic controller synthesis methodology, combining the essence of CDT and Hinfinity design. An important attempt reported in the literature on robust controller design for systems with structured uncertainties was to rearrange the controller synthesis problem into the mixed-sensitivity synthesis framework, and then to use Hinfinity synthesis tools. (Abstract shortened by UMI.)...