LMI-Based Stabilitity Analysis And Decentralized Controllers Design For A Class Of Interconnected Fuzzy Large-Scale Systems

By utilizing expert experience and language information, analyzing, modeling and control of many industrial complex plants can be handled effectively by fuzzy control technology, which otherwise will be very hard by approaches of traditional control theory, if not impossible. In addition, these complex plants can be controlled easily even without exact mathematical models, so fuzzy control has become a popular topic for analysis and design of complex nonlinear systems. However, the nonlinear nature of fuzzy control technology sets an obstacle to development of analytic method for stability analysis and systematic performance design of fuzzy control systems, and many design procedures are performed by trial-and-error. So, how to combine the advantages of analytic methods of traditional control theory and fuzzy systems theory and develop an integrated and systematic fuzzy control theory has increasingly becoming an urgent task for researchers of fuzzy control theory.On the other hand, with the rapid development of modern science and technology, the practical control system has become very huge and complex, so decentralized control theory of large-scale systems has attracted great attentions in both academic research and industrial applications. The main aim of this dissertation is to fuse the fuzzy logic control technology and decentralized control theory of large-scale system to develop a systematic design methodology that guaranteeing some basic requirements, such as stability and acceptable performance, for nonlinear interconnected fuzzy large-scale systems.Firstly, decentralized stabilization problems for interconnected fuzzy large-scale systems are considered. Stability and stabilization are the most basic problems in analysis and design of fuzzy control systems. The interconnected fuzzy large-scale systems considered in this dissertation consists of some interconnected T-S fuzzy subsystems, Decentralized Parallel Distributed Compensation (DPDC) fuzzy controllers are designed for this fuzzy large-scale systems, namely each T-S fuzzy subsystems will be controlled only by one PDC fuzzy controllers. Based on Lyapunov stability theory and decentralized control theory of large-scale systems, sufficient conditions for asymptotic stability of the closed-loop fuzzy large-scale systems are derived via LMI technology, and by using information of membership functions these LMI-basedsufficient conditions are relaxed and less conservative stabilization conditions are obtained. Considering that not all of the states variables of the system can be detected, decentralized states observers are also designed to estimate the system states. Similar to DPDC fuzzy controllers, these decentralized states observer are T-S fuzzy systems themselves. And LMI-based sufficient conditions for these states observers to estimate the true states of the fuzzy large-scale system asymptotically are developed. Furthermore, the well-known separation principle for designs of controllers and observers in linear system theory are proved to be hold for fuzzy large-scale systems considered in this dissertation, which is important for analysis and design problems of controllers and observers of interconnected fuzzy large-scale systems.Next, robust decentralized stabilization problems for a class of interconnected fuzzy large-scale systems with parametric uncertainties are considered in this dissertation, both for continuous-time and discrete-time case. The norm-bounded parametric uncertainties entered into system matrices, input matrices and interconnections in all of the T-S fuzzy subsystems. DPDC controllers are designed for the uncertain interconnected fuzzy large-scale systems and LMI-based decentralized robust stabilizable conditions for uncertain interconnected fuzzy large-scale systems are developed. By utilizing information of membership functions these robust stabilizable conditions are also relaxed and less conservative LMI-based conditions are obtained.In addition, decentralized stabilization problems for fuzzy large-scale...