Stability Analysis Of Fuzzy Large-scale Systems Of Uncertain Continuous Delays

With the rapid development of modern science and technology, and expanding productionscale, the controlled objects in actual control systems showing a high degree of complexity,nonlinearity and uncertainty, resulting in the building of systematic and exact mathematicalmodels becomes very difficult. Because the traditional control theory is based on the exactmathematical models of controlled object, so it makes traditional control theory difficult tocontrol these complex systems effectively. While the fuzzy control theory uses expert experienceand language information, it can control the systems in case of imprecise mathematical model, soit has gradually become one of the main methods for studying complex nonlinear systems. Inaddition, because the systems become more large-scale, and their dimensions become huger, itbrings considerable difficulties to our research. The appearance of large-scale systemsdecentralized control theory, and its making full use of structural information of systems, caneffectively solve the difficulties caused by high dimension.This thesis studies the stability of continuous-time uncertain fuzzy large-scale systems withtime delays by combining the decentralized control theory of large-scale systems and fuzzycontrol theory. The discussed fuzzy large-scale systems are constituted by a number of fuzzysubsystems, and each fuzzy subsystem is based on T-S fuzzy model. Through designing PDCcontroller for each T-S fuzzy subsystem to complete the controller design of entire fuzzylarge-scale systems, makes the studied fuzzy large-scale systems closed-loop asymptoticallystable. The main content of this thesis lies in the following two aspects:(1)Studied the stability of continuous-time uncertain fuzzy large-scale systems with timedelays and the time delays are in interconnections of fuzzy large-scale systems. Designeddecentralized parallel distributed compensation (DPDC) fuzzy controller for this fuzzylarge-scale systems, and gave the closed-loop asymptotic stability criteria relying on the timedelays’ derivatives, and finally transformed it into a set of linear matrix inequalities (LMI).(2)In engineering practice, the systems will always be more or less subject to interference ofthe external environment, so we must take into account the presence of external perturbationswhen modeling. Therefore, this thesis also studied the stability of uncertain fuzzy large-scalesystems with time delays and nonlinear perturbations. The time delays not only oninterconnections, but also on control input. Designed decentralized parallel distributedcompensation (DPDC) fuzzy controller for this fuzzy large-scale system by Lyapunov stabilitytheorem and decentralized control theory, and gave the closed-loop asymptotic stability criteriarelying on the time delays’ derivatives, and finally transformed it into a set of linear matrixinequalities (LMI).