BIBO STABILITY OF NONLINEAR FUZZY PI CONTROL-SYSTEMS

In this paper, we analyze in detail the bounded-input/bounded-output ( BIBO) stability of the nonlinear fuzzy proportional-integral (PI) cont rol systems developed in Ying, Siler, and Buckley (1990). In this inve stigation, the ''small gain theorem'' is employed to obtain a simple s ufficient condition on the global BIBO stability for general (stable a nd unstable) nonlinear control systems that possess finite gains and u nder the control of this type of fuzzy PI controlers. The derived suff icient condition provides a useful criterion for the design of such fu zzy PI control systems. In addition, we prove that in a conventional P I control system, if the linear PI controller is replaced by the nonli near fuzzy PI controller, the stability of the resulting control syste m remains unchanged This is true no matter the given process is linens or not. We will also derive some simple and explicit formulas for com puting the fuzzy PI controller parameters, using only the proportional and integral gains of the corresponding conventional linear PI contro ller This result makes the new sufficient condition very practical, be cause rising these formulas one can always replace a conventional line ar PI controller by a nonlinear fuzzy PI controller without altering t he system stability, to obtain better control performance.