Two-input-single-output fuzzy logic controllers: some global asymptotic stability results

This paper presents a global asymptotic stability analysis for two-input-single-output fuzzy logic controllers (FLC) where the controller output could be the result of a proportional-derivative (PD) or a proportional-integral (PI) fuzzy control strategy. In both cases, the input "rate of error" is defined as the output of a first-order filter. Based on input-output (I/O) properties of the inherent nonlinearity of such controllers, we employ quadratic Lyapunov functions together with strictly positivity realness assumptions to derive sufficient conditions of global asymptotic stability for closed-loop systems including a linear system and a FLC. These conditions are independent of the fuzzy rule base and the reasoning method provided the nonlinearity satisfies the properties used in the paper. Frequency interpretations of these conditions are also given, they lead to graphical tests.