Abstract
We prove that a fuzzy controller with linear control rules and Mamdani minimum inference is the sum of a global two-dimensional multilevel relay and a local nonlinear proportional-integral (PI) controller. The properties of the nonlinear gains of the local PI controller are investigated. Moreover, it is proven that, as the number of input fuzzy sets approaches ∞, the global multilevel relay approaches a global linear PI controller while the local nonlinear PI controller disappears.
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