Analysis of Fuzzy Nonlinearity - One Dimensional Case

Analysis of nonlinear dynamics of one-dimensional fuzzy control system is achieved indirectly. The fuzzy control law is decomposed into a linear control law and a superimposed nonlinearity. The linear part is treated as variable-level bang-bang control and analyzed by applying Lyapunov stability theorem. Superimposed nonlinearity can then be categorized according to its effects on the stability and transient performance of the closed loop system. With fuzzy nonlinear control law formulated explicitly, the design parameters can then be synthesized to satisfy control system requirements.