The Method Of Design On The Stability Of Fuzzy Systems

In this paper, we take a predator-prey system with Holling II functional response function for an example. Two different methods were used to guarantee the stability of the system.Firstly, we found fuzzy dynamic model and construct an adaptive fuzzy controller by fuzzy logic. In order to overcome the complexities came from the outer environment, the direct controller was added as an upervisory controller which makes the adaptive fuzzy controller steady. We prove the stability of the closed-loop system by Lyapunov stability theory. The goal is to make practical output track ideal output. It provides an effective means for the biological control by designing a stable adaptive fuzzy controller to control the number of three types of populations within the range of aspirations.Secondly, specify the fuzzy systems structure and parameters to ensure closed-loop system is stable. Based on the fuzzy Lyapunov synthesis method proposed by M.Margaliot and G.Langholz and K-means algorithm, this article introduces a new method to design a stable fuzzy systems. Firstly, according to fuzzy Lyapunov synthesis method establish original fuzzy rules, and then calculate the cluster center to optimize fuzzy rules by K-means algorithm. In the end, computer antecedent fitness of every rules and the fuzzy rule number to establish a stable fuzzy system. This method guarantees system's stability and optimized the system. This method has raised a new road for fuzzy systems research.