Dissipative Control Problem For Singular Systems

It is well known that the singular system has higher capability to describe physical system, and it is a kind of dynamical systems of more general and has widely applied background. Singular system models are more convenient and natural than normal models such as interconnected large-scale systems, economic systems, electrical network, power systems, chemical processes and so on. This is the reason why singular systems have attracted much interest in recent years, and they have been developed sufficiently.Dissipative theory plays an important role in the stability research of control systems since it was brought forward in 1970s, the implication is that there exists a nonnegative energy function (namely storage function) such that the energy consumption of a control system is always less than the supply rate of the energy. A kind of design and analytic idea is put forward in the dissipative theory, i.e. from the point of view of energy, and energy is described by input and output. Dissipative theory can contact some mathematic tools with physical phenomenon, and has been applied to many control problems. Dissipative theory has been approved to be a kind of effective method in machine system, robot control and adaptive control, nonlinear H_∞ control and so on.This thesis focuses on the problems of dissipative control for singular systems and is organized as follows:(1) The main background of the problem discussed in this thesis is introduced. Firstly, a brief introduction to singular systems is given, and some examples of singular systems are presented to illustrate the wide application in various fields; Secondly, the problems of dissipative control and passive control are introduced. Finally, the main work is summarized.