Non-fragile Decentralized Control For Singular Large-scale Systems With Time-delay Based On LMI Approach

A class of systems with extensive form has been paid special attention by the researchers, because of the wide application of modern control theory and method in engineering system and the infiltration in other field of learning. It is called "singular large-scale system", which corresponds with the normal system. Decentralized control descriptor systems can be regarded as the natural extension of general decentralized control systems or another form of singular large-scale systems. Decentralized control obviously avoids the faults of the complex information changes, hard-line control of centralized control. So, the application of decentralized control has a bright future. In order to more accurately describe the actual system, we must also consider the delay and the uncertain phenomenon. On the other hand, in actual engineering, controller’s parameters can’t be exactly implemented when the controller will be influenced by all kinds of factors in the process of the controller’s digitizing, and the small changes of the controller gains may result in performance degradation or damage stability of closed-loop systems. So, we should design non-fragile controller for uncertain descriptor systems.In this thesis, non-fragile control problems aiming at singular large-scale systems with time-delay are discussed successively under the two classes of gain perturbations, namely, additive and multiplicative by linear matrix inequality (LMI) approach. Some positive results are gained. The main contribution of this thesis is summarized as follows:1. The background of this thesis is introduced. Firstly, outlines the development of the singular system and singular large-scale system, and also the research projects in the current situation. Then research situation and actual background of non-fragile control for singular large-scale systems are given. Finally, the main work is summarized. 2. This article describes the foundations of mathematics involved and the relevant prior knowledge. Theorems of stability and singular systems are primitively introduced. Meanwhile, some knowledge on matrix inequalities common used in the thesis is summarized.3. The non-fragile decentralized control problem of the singular linear large-scale system with delay-time is investigated. Firstly, the non-fragile stabilization controllers of the singular linear system with delay-time are given via LMI method. On that basis, the singular linear large-scale system with delay-time is studied. The non-fragile decentralized stabilization controllers are designed, which make the closed-loop systems regular, robustly stable and impulse-free. Finally, a numerical example is give to illustrate the validity of proposed method.4. The non-fragile decentralized robust control problems of uncertain singular linear large-scale system with delay-time are studied. Similarly, uncertain singular systems with delay-time and uncertain singular linear large-scale system with delay-time are designed via LMI method, which make the corresponding closed-loop systems regular, robustly stable and impulse-free. Finally, a numerical example is give to illustrate the validity of proposed method.5. Summary and Outlook. A summary of this thesis is given. At the same time, we give an expectation for the future work.