Stability of interpolative fuzzy KH-controllers

The classical approaches in fuzzy control (Zadeh and Mamdani) deal with dense rule bases. When this is not the case, i.e. in sparse rule bases one has to choose another method. Fuzzy rule interpolation (proposed first by Koczy and Hirota, 1993, 1996) offers a possibility to construct fuzzy controllers (KH-controllers) under such conditions. On the other hand there is a great demand in finding a stable interpolating method among researchers in the field of mathematical (numerical) analysis. We would like to approximate a function that is only known at distinct points (e.g. where it can be measured). In practice the stability of these method is a natural requirement. The classical methods generally do not fulfill this condition, only with some strong restriction concerning the measured points. If we neglect the classical form of the approximating function (polynomial and trigonometrical), we can get better behaving approximation. The function of the KH-controller approximating function (which is a simple fractional function) fulfills the stability condition