Regularization And Stabilization Of Rectangular Descriptor Decentralized Systems

Rosenbrock brought up the concept of the singular systems in studying the network systems of complex circuits for the first time in 1974, and later, in the fields of economic management, electrical network, biologic engineering and aerospace technique and so on, people find the examples of descriptor systems. And the descriptor decentralized systems are not only the natural extend of the normal decentralized systems, but also one form of the descriptor systems. When the modeling is incomplete, some states are unknown or broken-down; the models have the rectangular structure usually. In the light of recent work on the theory of descriptor systems, this thesis provides a systematic study on the problems of the regularization, freeness of impulse and stabilization of rectangular descriptor decentralized systems.The main contribution of this paper includes:1. Survey the current development and research harvests internationally of the descriptor decentralized systems, and then bring up the opinions.2. Some problems on the regularization, freeness of impulse for the rectangular descriptor decentralized systems are studied. Via using dynamic compensation and decentralized output feedbacks, then by simple algebraic transform, the problem is equivalently converted into corresponding problem of the normal descriptor decentralized systems. Two necessary and sufficient conditions for making closed-loop systems both regular and impulse-free are given, and two different controllers are constructed.3. Based on the regularization and freeness of impulse, the problem of stabilization for the rectangular descriptor decentralized systems is discussed. The rectangular systems are converted into the square ones using dynamic compensation, and then the finite decentralized fixed mode and impulsive decentralized fixed mode are defined. And then, necessary and sufficient conditions to stabilize the closed-loop systems are presented by using decentralized output feedbacks.The present work is a natural extension of that for the square decentralized control systems. Some numerical examples are given to illustrate the design procedures.