Dissipative Analysis And Control Problem For Descriptor Systems

Dissipative property is often seen as input-output property in the dynamic pro-cess of descriptor systems. It embodies the attenuation characteristic of descriptor system under bounded exogenous input. Researching the dissipative control of de-scriptor system will be important for both theory and application, because the bulk of dynamic systems with attenuation characteristic are met in dynamic process. In addition, there may be uncertain and time-delay in systems due to modeling error, linearization, data error and delay of signal transmission, so it is necessary to study the dissipative control of uncertain descriptor systems and delay descriptor systems.By using linear matrix inequality (LMI), the paper discusses on the dissipative problem for descriptor systems, the main contribution of this paper is summarized as follows:(1) The main background of the problem discussed in this dissertation is in-troduced. Firstly, the structure characteristics and application background for de-scriptor systems are introduced, and many practical examples are given to illustrate the extensive existence of such systems in engineering. Then the development and recent progress are presented for descriptor systems. Furthermore, the significance and recent development of dissipative control problem are reviewed, at the same time, some relative knowledge of derivative and proportional state feedback control theory and linear matrix inequality(LMI) is introduced, so are the mainframe and main method. Finally, the main work of this dissertation is listed.(2) The mathematical definitions for dissipative descriptor systems and pas-sive descriptor systems discussed in this dissertation are introduced. By using the definitions, the relationship between dissipation and positive real and bounded real for descriptor systems are investigated.(3) The dissipative control problems are considered for descriptor systems. dis-sipative control is firstly discussed for dissipative systems without uncertainty, and the conditions for the closed-loop systems to be admissible and strictly dissipative are proposed in the cases of state feedback control and derivative and proportional state feedback control. Then robust dissipative analysis and control are discussed for descriptor systems with linear-fractional parameter uncertainties. The design of two types of controllers is presented for the closed-loop systems to be generalized quadratically stable and robust strictly dissipative.(4) The dissipative control problems are discussed for descriptor systems with time-delay. dissipative control is firstly discussed for dissipative systems without uncertainty under the delay-independent case and the delay-dependent case, re-spectively. And the conditions for the closed-loop systems to be admissible and strictly dissipative are proposed in the cases of memory (memoryless) state feed-back control and memory (memoryless) derivative and proportional state feedback controller. Then robust dissipative analysis and control are discussed for delay de-scriptor systems with linear-fractional parameter uncertainties. The design of four types of controllers is presented for the closed-loop systems to be generalized systems quadratically stable and robust strictly dissipative.(5) The dissipative control problems are studied for a class of non-liner de-scriptor systems without and with time-delay, respectively. At first, the condition for asymptotically stable of the class descriptor without time-delay is given, and state feedback controller and derivative and proportional state feedback controller are designed to make the systems be stable and dissipative. Then robust dissipative analysis and control are discussed for delay descriptor systems with linear-fractional parameter uncertainties. At the same time, the condition for asymptotically stable and dissipative of the class descriptor with time-delay is given, then the correspond-ing controller are presented.(6) A summary of this paper is given. At the same time, we give an expectation for the future work.As to the conclusions obtained in the paper, simulation examples are presented to show the useness and effectiveness of the proposed methods.