An estimation of the stability domain of a fuzzy controlled pendulum using overlapping attractors and vector norms

The design of stable fuzzy controllers can be achieved by determining a series of embedded sets for which the attractor of any set is included into the next set of the series. The framework of the comparison principle, along with overvaluing systems and vector norms, allows the computation of the attractors and to handle the robustness with respect to uncertainties. Considering the inverted pendulum control problem, this procedure is applied to the parameter tuning of a fuzzy controller with singleton defuzzification, whose regionwise structure leads to a rational partition of the state space