Analysis of structure and stability for the simplest two-dimensional fuzzy controller using generalized trapezoid-shaped input fuzzy sets

By summarizing the common characteristics of popular triangular and trapezoidal fuzzy sets, the more extensive generalized trapezoid-shaped (GTS) fuzzy set has been proposed. We have contributed to the analytical structures and stability analysis of the simplest two-dimensional fuzzy controllers using GTS input fuzzy sets. This class of fuzzy controllers is a combination of a piecewise linear PI controller plus a piecewise constant term. Based on the mathematical structures, the bounded-input bounded-output (BIBO) stability conditions for fuzzy control systems have been obtained by the well-known Small Gain Theorem. Two computer simulations are provided to demonstrate that the new fuzzy controller is effective and superior to the conventional PID controller.