Stability analysis of nonlinear fuzzy PI control systems

In this paper, we analyze the stability of nonlinear fuzzy PI (proportional-integral) control systems. The fuzzy PI controller involved is actually a nonlinear adaptive PI controller whose gains change continuously with output of the processes under control. We have employed the “small gain theorem” to obtain a simple sufficient condition for the global asymptotic stability of the nonlinear fuzzy PI control systems. In addition, we have proven that in a conventional PI control system, if the linear PI controller is replaced by the nonlinear fuzzy PI controller, then the stability of the resulting control system remains unchanged. This result is true no matter the given process is linear or not. We have also derived explicit formulas for the computation of the fuzzy PI controller parameters, using only the proportional and integral gains of the corresponding linear PI controller