Non-fragile Decentralized Control For Singular Large-scale Systems

In recent years, the singular large-scale systems'control problems gradually become the popular research problem in the control theorists. Because of the particularity of singular system, the research on the control problem needs to consider not only stability but also regularity and impulse (for continuous time case) or causality (for discrete time case). So, singular large-scale systems are more difficult to control than normal large-scale systems. And the singular large-scale systems are difficult to be centralized controlled due to their some obvious characteristics, enormous dimensions, multitudinous elements and busy information changes between subsystems, etc, so it is instead of using decentralized control for singular large-scale systems. Decentralized control is to use multiple controllers to replace centralized controller and each of the controllers just measures the output of the responding subsystem, and just controls the input of the responding subsystem and this decentralized structure obviously avoids the faults of the complex information changes, hard-line control and the high cost of communication of centralized control. So, the application of decentralized control has a bright future.In actual engineering, controller's parameters will change to a certain degree when the controller will be influenced by all kinds of factors in the process of the controller's digitizing, and then this will influence the accurate realization of the controller. Therefore, even if the controller for the system object's uncertainties is robust, the controller for uncertainties of its own is fragile. In this situation, it needs to design non-fragile controller to make the close-loop system still keep a better robustness and stability when controller gain produce perturbation. So, the research on non-fragile control problem has very important practical significance.At present, the non-fragile control problem is researched mainly in the normal system and singular system, and especially for normal system of non-fragile control studies, it has gain plenty of positive results. But this problem has hardly any researches in singular large-scale systems, and a lot of problems remain to be researched and solved.In this thesis, non-fragile control problems aiming at linear singular large-scale systems are discussed successively under the two classes of gain perturbations, namely, additive and multiplicative by Lyapunov approach and linear matrix inequality (LMI) approach. Some positive results are gained. And using MATLAB software and LMI toolbox simulation results prove the effectiveness and feasibility of all the results.