Fuzzy Control Based On Discrete T-S Hyperbolic Systems

Since fuzzy logic system was proposed, the study of complex nonlinear systems has had a great breakthrough. It utilized fuzzy mathematics thought to deal with nonlinear systems containing uncertain information which cannot be represented accurately by mathematical tools, and has been widely applied to various fields of society. Therefore, fuzzy control theory and methods based on fuzzy logic system become one of the core of the control. With the constantly improvement of the theory, T-S fuzzy linear system theory, T-S fuzzy bilinear system theory and T-S fuzzy nonlinear system theory were presented successively. Because of the complexity of the external environment, there were many adverse factors such as uncertainties,time delays or stochastic disturbance in a T-S fuzzy system, which seriously affected the system performance and even made the unstable system.Based on the Lyapunov stability theorem, parallel distribution compensation(PDC) method and non-PDC, robust H￥control theory, combining linear matrix inequality(LMI) techniques, Schur theorem and so on, we study stability analysis for T-S fuzzy hyperbolic system, and make it meet certain performance.The main contributions can be generalized as follows:Firstly, a novel discrete T-S fuzzy hyperbolic model is presented for a class of discrete nonlinear systems, the consequence of which is a hyperbolic tangent dynamic model. First, based on Lyapunov theorem theory and PDC, a novel fuzzy hyperbolic controller is designed to gain the stability conditions of the closed-loop system via linear matrix inequalities(LMIs). Then according to the robust H￥theory, the asymptotically stable condition of the closed-loop system with external disturbance is made. Comparing with the control method based on discrete T-S fuzzy linear model, the novel control method can achieve much smaller control amplitude when the stabilization time is almost the same. The control method can be called as “soft” constraint control method.Secondly, by applying the “soft” constraint control approach based on discrete T-S fuzzy hyperbolic model and non-PDC, and constructing non-quadratic Lyapunov function, the robust stability analysis of the discrete T-S fuzzy hyperbolic system with uncertain parameter are realized. Comparing with the non-PDC control method based on T-S fuzzy linear model, the fuzzy hyperbolic control method can achieve much smaller control amplitude.Thirdly, the T-S fuzzy hyperbolic tangent stochastic system model is established, and the “soft” constraint control method is generalized to stochastic systems. A generalized 2H fuzzy control is designed based on PDC to gain the mean-square stable conditions of stochastic system. Comparing with the existing method, the control approach presented in the chapter can achieve much smaller control amplitude. Especially, when time delay exists in the stochastic system, the control approach proposed still can make the closed-loop stochastic system be stable with generalized2 H performance.