Delay-Dependent Decentralized Robust Control Of Interconnected Systems

Delay interconnected systems can be seen everywhere in practice. As developing of science and technology, the research of delay interconnected systems has been deepened continuously. This dissertation will study delay-dependent decentralized robust control for delay interconnected systems.Firstly, a survey is given to illustrate the background and the research directions of delay interconnected systems. Then, a series of researches are given. They are, decentralized robust stabilization of delay interconnected systems, decentralized passive control of interconnected systems, and decentralized robust H_∞ control of delay interconnected systems. Based on the theoretical results, decentralized control of delay power systems is studied. At the end, a summary and a prospect of the research are given.In the dissertation, following tools are used: delay difference inequalities, comparison principle, Lyapunov-Krasovskii functional method, delay integral inequalities and Linear Matrix Inequality (LMI) method. Combining these tools, this dissertation will give some new results.By using Lyapunov-Krasovskii functional and delay integral inequalities, the decentralized robust stabilization for continuous-time linear interconnected systems is studied. The LMI-based delay-dependent conditions are obtained. Constructing special Lyapunov-Krasovskii functional and using delay integral inequality and LMI, the decentralized robust stabilization for a class of nonlinear interconnected system with separated variables are studied. It illustrates that LMI can be applied to some kind of nonlinear systems. A comparison principle and new delay difference inequality are presented for high dimensional discrete systems. Based on these tools, robust stabilization and decentralized robust stabilization are studied for uncertain discrete systems and discrete interconnected systems with multiple delays. Some delay-dependent sufficient conditions are given for the robust stabilization and decentralized robust stabilization of the discrete systems by means of output feedback.Using model transform and special Lyapunov-Krasovskii functional, passive decentralized robust control is studied for interconnected systems with interconnected delays. New existence and constructive delay-dependent criteria are proposed to design the decentralized controllers. Some numerical examples are given to illustrate the availability of the method. Constructing special Lyapunov-Krasovskii functional...