A method to construct P-type Lyapunov function of model-based fuzzy system

In this paper, the stability problem of a model-based fuzzy system put forward by Tanake and Sugeno (1992) is discussed. By means of transforming it into a contracting problem of convexes V_a, some difficulties of judging and constructing the Lyapunov function are overcome. In addition, an auxiliary method to estimate convexes is established, which contributes a lot to the research. From the research paper, two important results are derived. The first is that whether a model-based fuzzy system exists, a P-type Lyapunov function can be determined by the algorithm. The latter is that if it has a P-type Lyapunov function, one of them can be constructed by the algorithm. Furthermore, the results can also contribute to local linearization of nonlinear systems