Controllability Problem For Rectangular Descriptor Decentralized Systems

Since the British professor Rosenbrock H. H. brought up the concept of the descriptor systems for the first time in1974, the descriptor systems begin its research. The descriptor systems exist in the fields of power systems, electrical network and aerospace systems and so on. Besides, the descriptor decentralized systems are not only the natural extension of the normal decentralized systems, but also the forms of the descriptor systems. And we can see the models are incomplete, some states are unknown or broken down in the practical models, and the models usually have the rectangular structure. But there are no literatures discuss the problem of the regularization, controllability and observability about the descriptor decentralized systems at present. So this thesis provides a systematic study on the problem of the regularization, controllability and observability on the base of the theory of rectangular descriptor systems.The main contributions of this thesis include:1. Survey the current development and research harvests internationally of the descriptor decentralized system and rectangular descriptor system, and then explain the theory value and practical significance, and bring up my own options.2. Some problems on the regularization and regularizable for the rectangular descriptor systems are studied. First, the definition of regularization is presented, because some systems are not regularization, the definition of regularizable is brought up. Second, it also discusses the necessary and sufficient conditions for making the systems regularizable under the different output feedbacks, and the main feedback of these are static output feedback, dynamic output feedback and mixed output feedback and so on. And on the base of that, the mixed output feedback controller is devised. After all, we can find the controller by a "trial and test" procedure.3. The problems of controllability and observerbility are discussed on the base of the systems regularization. First, the definitions of controllabilities and observerbilities of the systems are brought up, and then, the necessary and sufficient conditions for satisfying conditions of the controllabilities and observerbilities are discussed. Finally, some numerical examples are given to illustrate the feasible of the results.The results of this thesis are the natural extension of rectangular descriptor systems, and in theory, the results also reach an agreement with the results of the descriptor decentralized systems, due to the characters of regularization, controllability and observerbility are possessed by the systems themselves. Some numerical examples illustrate the effective and feasible of the results.