On the simplest fuzzy two - term controller structure derived via algebraic product t-norm -bounded sum t-conorm - Mamdani minimum inference combination

Abstract

Patel and Mohan (2002, Automatica, 38, 981-993) state that the analytical structure of the simplest fuzzy PI controller, derived via algebraic product t-norm, bounded sum t-conorm and Mamdani minimum inference, is not suitable for control purpose. Here we show that the above statement is incorrect, and the above analytical structure is very much suitable for control. Moreover, using the well-known Small Gain theorem we establish suf£cient conditions for bounded-input bounded-output (BIBO) stability of feedback systems containing the above controller as a subsystem.