Stability Analysis And Controller Design Of Fuzzy Systems With Time Delay

With the development of science and the progress of society, the modern control theorycan hardly meet all application requirements in social production activities, in particularwhere uncertainties and external disturbances exist. Fuzzy theory which was firstly proposedin 1965 is bringing new opportunities and developments to the control theory. As time delay isvery common in control systems and its existence will directly affect the system performance,the study of fuzzy control systems jointly with time delay is wide range of theoretical andpractical significance. At present, although a lot of results on fuzzy system with time-delayhave been concluded, there are still many aspects to be further researched and shortcomings tobe resolved.In this thesis, the problem of stability analysis and controller design of a class of T-Sfuzzy systems with interval time-varying delay is investigated. Based onLyapunov-Krasovskii functional and by introducing two new variables to avoid boundingtechnique, the results are given in the form of linear matrix inequalities.In this article, we will research and improve in the following aspects:First we propose the background and significance of the research on the theory of fuzzysystems, and systematically review the development of the T-S fuzzy systems with time-delay,stability theory and linear matrix inequalities. Then, the knowledge of preparation of thisthesis as well as some important lemmas is introduced.Based on the Lyapunov stability theory, the delay-dependent stability criteria of T-Sfuzzy systems with interval time-varying delay are given. Firstly we get a less conservativeresult than the some existing ones by using the free matrix approach, and then get a moresimple result without introducing any free matrix. At last the comparisons between the twomethods are given.The problem of robust stability of a class of fuzzy system with time-delay and parameteruncertainties is discussed. Firstly, forms of system parameter uncertainties are introduced. Theform of the norm-bounded and polytopic are introduced to analysis the robust stability offuzzy system. The less conservative robust stability criteria in form of linear matrixinequalities are obtained. And the differents between simulation and computationalcomplexity are showed by numerical examples.Consider the controller design of fuzzy systems with time delay. This paper mainlystudied a class of fuzzy systems with parameter uncertainties and external disturbance.Making use of the robust stability analysis methods in pervious part to conduct analysis on the H_∞performance, a less conservative stability criterion meeting the givenH∞performancerequirements is gained. To have the controller designed, fuzzy PDC method is used and asufficient condition in form of nonlinear matrix inequalities on controller existence isacquired. The controller is designed based on LMI-based iterative algorithm which does notneed to adjust any parameter. A feasible solution can be computed after each iteration. Thesimulations of numerical examples verify the effectiveness of the algorithm. Finally, thecontent of the thesis is summed up and prospect of further study is proposed.