H_∞ Reduced-Order Controller Design For Descriptor Systems

It is well known that the descriptor systems have higher capability to describe physical system with widely applied background. So a great deal of interest has been devoted to the study of descriptor systems, and there have been many results for descriptor systems. This thesis studies the problems of the H_∞reduced-order controllers for descriptor systems and H_∞control for rectangular descriptor systems. Some new design techniques are proposed. The main contents in the thesis are as follows:1. The H_∞reduced-order controller design for general square descriptor systems is studied, and two methods are present. Firstly, according to the reduced-order controller based on coprime-fraction and restricted system equality for descriptor systems and the condition for H_∞control, the reduced-order controller design problem is converted to the matrix inequality solvable problem. A design method and existence condition of H_∞reduced-order controller for descriptor systems is obtained. Secondly, further reduced-order controller is concerned, which is based on the condition of dynamic order for the existence of controllers of descriptor systems and general bounded real lemma for descriptor systems, and a design method and existence condition of reduced-order controller which satisfies the condition of dynamic order are obtained. This method is shown to be effective by numerical examples.2. The H_∞control for rectangular descriptor systems is studied. On the one hand, this part generalizes the H_∞control theory for square descriptor systems to rectangular systems, and provides a sufficient condition of H_∞controller for rectangular descriptor systems based on algebraic Riccati inequality. On the other hand, the full-order and reduced-order H_∞controller design for rectangular descriptor systems is studied, and two kinds of full-order controller design methods and a reduced-order controller design method for rectangular descriptor systems based on the new restricted system equality and general bounded real lemma are given, which is fit for general rectangular descriptor systems without any assumptions on systems.