On the persistency of excitation in fuzzy systems

Fuzzy systems have been developed for more than two decades. Recently there appeared a number of results of fuzzy systems regarding the modelling and identification. Making use of the property that the consequence parameters are linear in fuzzy systems, recursive least squares algorithms are commonly adopted for training or adaptation of fuzzy systems. The condition for convergence of the parameters requires that the regressor vector are persistently exciting. This paper aims to show persistency of excitation in fuzzy systems.