On the stability of fuzzy control rulebase for a nonlinear process

In this paper, an input-output stability analysis is developed for a nearly linear plant. In the stability analysis, the implicit equilibrium states are studied, instead of the zero equilibrium state of an unforced system, in the classical sense. The system being analyzed is actually being driven by fuzzily derived controlled inputs. The stability of such a system is referred to as the stability of a fuzzy controlled system. It is assumed that the nonlinear process model is available either for analysis or for design. A nearly-linear assumption is verified for a class of physical process set-point control processes. This is essentially the method of diminishing nonlinearity. Once this is verified, it remains to show that the linear part of the system is dissipative from an input-output point of view. The stability requirements are verified analytically, where possible or via simulation. The application of the theorem extends to a rule-base designed either by the operator manual type IF-THEN rules or other more systematic design approaches, as long as an approximate model of the process is available for analysis