A Study Of Mandani Fuzzy Systerm Based On Markov Chain

The fuzzy system is essentially non-linear, so its stability and indicators of the stability analysis are often more difficult to analyzed. Until now, many scholars make a lot of work in the stability theory of fuzzy systems, however, a complete theoretical system is still not established, and there are many theoretical issues need to be further studied. This article aims to study stability analysis and design of fuzzy controller systematically, gets some inspiration in the experiment and a new idea for the study of fuzzy control system stability analysis.First, this paper introduces the overview of fuzzy control system systematically, summarizes the relevant theoretical methods and scientific research on the stability analysis of fuzzy control, and evaluates the affect of these research methods on the later work briefly.Second, this paper introduces the method of T-S fuzzy control system stability analysis. For the T-S fuzzy controller on the basis of Lyapunov stability theory, it gives the continuous fuzzy system, the discrete fuzzy system in open loop and closed-loop stability conditions, and gives a sufficient condition when closed-loop system is stable. But it is not easy to find positive definite matrix P. By introducing linear matrix inequalities (LMI) to seek LMI solution of the problem can transform this problem to solving LMI, therefor reduces the solving difficulty. On the LMI conditions, the paper studies the sufficient condition of stability for T-S type continuous, discrete fuzzy system in open loop as well as the related conclusions.Third, the paper establishes a Markov process model of the system output sequence on the basis of Markov process by analyzing the structure of the closed-loop system, and use Markov process mature results to analyze output sequence of the system, and find the relationship between the controller and the output by statistical output sequence inversely. On these conditions, the type of controller would not be restricted, chooses the Mandani type as the research object. Based on the above ideas, the study found that under the conditions of the stability of the system, the sufficient condition in the probability for the convergence speed of the fuzzy controller output.Finally, in response to these above findings, it selects the Mandani type system, and simulates experiments, then gets simulation diagram. So the method has a certain effect, and provides a guideline for future research.