Stability analysis of discrete fuzzy control system

The stability of a discrete fuzzy control system is discussed. A fuzzy control system has a linear plant but a nonlinear controller. The nonlinear fuzzy controller is based on an indirect reasoning mechanism. Nonlinearity of the fuzzy controller is characterized by a linear gain using a sector condition. The stability of the system is checked against the sector, whose lower bound is decided according to an algorithm for selecting the lower sector based on actual conditions. A condition of absolute stability is derived for the system. It is shown that the parametric space related to the universe of discourse in which the absolute stability of the system is guaranteed becomes wider if a sector is chosen based on the algorithm. A sufficient condition of absolute stability is derived for the case of two inputs and a single output. The effect of initial conditions and sampling time is qualitatively discussed