Affine Uncertain Singular Systems Robustness Dissipative Analysis And Control

Singular system is a kind of more general dynamic system and has extensive applied background. It has been used to describe many real systems, such as economic system, electical network, electrical power system, robot system, spacecraft system and so on. Therefore it has important both theoretical and practical value to study singular system theory.Dissipative theory plays an important role in the research of control systems. Its nature implication is that there exists a nonnegative energy function(namely store function) such that the energy consumption of a control system is always less than the given supply rate of the energy. In fact, dissipative theory generalizes the circle criterion theorem, Kalman-Yacubovitch lemma, bounded real lemma and passivity theory.In practical engineering control systems, the existence of uncertainties is objective and inevitable because of the effects of modeling error, measuring error, the variation of working environment and so on. These uncertainties often destroy the stability of control systems or make that some other system performances cannot hold any more. So it is very necessary to consider the problems of robustness analysis and synthesis for control systems with uncertainties.This thesis mainly deals with the problems of robust dissipativeness analysis and robust dissipative control for singular systems with affine uncertainties. By means of generalized parameter-dependent Lyapunov function and linear matrix inequalities (LMIs), several sufficient conditions are obtained to guarantee the generalized quadratic stability and strict dissipativeness of the singular systems with affine uncertainties. And the relationships among the above conditions are analysed and discussed. Moreover, by using parameter-independent and parameter-dependent Lyapunov function, respectively, the existence conditions of a state feedback robust dissipative controller are presented by LMIs, and the explicit expressions of the controller are also given in terms of the solutions of LMIs, which guarantee that the closed-loop affine uncertain singular system is generalized quadratic stable and strictly dissipative. All the above theoretical results have been illustrated through numerical examples.