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) control systems developed in Ying, Siler, and Buckley (1990). In this investigation, the "small gain theorem" is employed to obtain a simple sufficient condition on the global BIBO stability for general (stable and unstable) nonlinear control systems that possess finite gains and under the control of this type of fuzzy PI controlers. The derived sufficient condition provides a useful criterion for the design of such fuzzy PI control systems. In addition, we prove that in a conventional PI control system, if the linear PI controller is replaced by the nonlinear fuzzy PI controller, the stability of the resulting control system remains unchanged. This is true no matter the given process is linear or not. We will also derive some simple and explicit formulas for computing the fuzzy PI controller parameters, using only the proportional and integral gains of the corresponding conventional linear PI controller. This result makes the new sufficient condition very practical, because using these formulas one can always replace a conventional linear PI controller by a nonlinear fuzzy PI controller without altering the system stability, to obtain better control performance. © 1997 IOS Press.