Dynamic Output Feedback Stabilization And Robust Stabilization Of A Class Of Affine Nonlinear Singular Systems

Singular systems are a class of important systems in engineering applications. Since 1970s, many scholars in the world have been attracted to the research on the theory and application of singular systems, and a great progress has been made. With the development of the research, it is found that many practical systems, such as economic systems, robot systems, constrained mechanical systems, power systems and so on, have singular systems. Nearly complete theoretical framework has been established for linear time-invariant singular systems. Compare with the research on linear singular systems, however, the development of nonlinear singular systems is so slow that the results of fundamental theory are very few over the past decade. Especially in the basic theory, the study results are less.This thesis focuses on the dynamic output feedback controllers for affine nonlinear singular systems and the robust control problem of affine nonlinear singular systems.The main content could be summarized as follows:1. This thesis introduces the basic concepts and knowledge of mathematics for affine nonlinear singular systems, which gives the knowledge to provide the necessary structure for studying and researching of the large number of scholars.2. The problem of dynamic output feedback for affine nonlinear singular systems is considered. This thesis gives necessary and sufficient condition for existence of dynamic output feedback controllers, and gives a dynamic compensator for a class of affine nonlinear singular systems, and discusses the asymptotic stability of the closed-loop system, which will provide a basis for engineering. Finally, numerical example proves the validity of theorems.3. The problem of robust stabilization for affine nonlinear singular systems is considered. In this thesis, the affine nonlinear singular systems are transformed into normal affine nonlinear systems via change of systems, and the Lyapunov stability of systems is studied. This thesis gives a necessary and sufficient condition for robust stabilization of a class of affine nonlinear singular systems whose regular is starting point, and obtains the close ties between the system robust stabilizability and the existence of positive solutions of HJI differential inequality.