Guaranteed Cost Control For A Class Of Uncertain Singular Large-Scale Systems With Interconnected Time Delay

The design and analysis of interconnected large-scale system has been a main and difficult issue in the field of control theory. It is more significant and more challenging to do some research on interconnected large-scale systems which exist in many fields, such as communication systems, power systems, transportation systems and are characterized by high dimension, complicated structure, uncertainty and time delay. In addition to stability, a control system should meet some more demands, so the concept of guaranteed cost control for system is put forward. A lot of perfect results concerning the guaranteed cost control of normal system have been gained, by comparison, fewer satisfying results concerning the same issue of a singular system have been gained. In this paper, the guaranteed cost control problem for a class of uncertain singular large-scale systems with interconnected time-delay is mainly discussed. The main structure of this paper is as follows:In chapter 1, the research background and achievements of the large-scale system, singular systems, time-delay systems and guaranteed cost control are introduced respectively.In chapter 2, the fundamental knowledge of linear matrix inequality and Lyapunov stability are introduced.In chapter 3, the guaranteed cost control problem of uncertain singular large-scale systems with interconnected time-delay is discussed. Based on Lyapunov function, combined with the method of linear matrix inequality, the sufficient condition and design method for the existence of guaranteed cost state feedback controller are derived. Finally, the simulation is given to illustrate the validity of the proposed method.In chapter 4, the delay-dependent guaranteed cost control problem of uncertain singular large-scale systems with interconnected time-delay is considered. Based on Lyapunov function and linear matrix inequality, a delay-dependent sufficient condition of the state feedbacke guaranteed cost controller is proposed adopting integral inequality, and the controller design method is provided. Finally, a simulation example shows the validity of the method.In chapter 5, the guaranteed cost control problem of uncertain singular large-scale systems with interconnected multiple time delays are discussed. The sufficient condition for decentralized state feedback guaranteed cost controller and design method are given using Lyapunov function and linear matrix inequality. At last, a simulation example shows the validity of the method.