| Descriptor systems is a more accurate description for a class of systems existed in the engineering field and the social and economic field, and is a class of more general dynamic systems than normal systems. From 1970s when the concept of descriptor systems was first put forward to now, throughout the development for thirty years, more and more natural characters of descriptor systems have been discovered. In the light of recent work on the theory of descriptor systems, this thesis provides a systematic study on the problems of the finite pole assignment of rectangular systems and the stabilizability for descriptor systems via static output feedback. The main contents in the thesis are as follows:1. The finite pole assignment problem for rectangular systems based on dynamic compensator is studied and two finite pole assignment approaches are proposed. The main difference between them is the form of dynamic compensator. This results in that the finite pole assignment approach and necessary and sufficient condition are different. The number of finite poles assigned for rectangular systems based on dynamic compensator is also obtained. Via dynamic compensator, a rectangular system is either directly transformed into a normal system or first transformed into a square descriptor system, then into a normal system. At last the whole closed-loop system achieves regularity and freeness of impulse as well as arbitrary pole assignment.2. The stabilizability problem for descriptor systems via static output feedback is studied. Based on the generalized Lyapunov equations, a necessary and sufficient condition and some related corollaries are given for the stabilizability of descriptor systems. Compared to normal systems, the conclusion in the thesis is more general and extends corresponding one about output feedback stabilizability for normal systems. An algorithm is given to obtain stabilizing controller parameters, which is shown to be effective by numerical examples. |
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