Discretizing Continuous-time Controllers with Fuzzy Logic Systems and Its Stability Analysis

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous-time controller in computer-controlled systems. All the continuous-time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new smooth controller that can replace the original controller, independent of the sampling time under the Sampling Theorem. Consequently, the proposed controller not only can discretize the continuous-time controllers, but also can tolerate a wider range of sampling time uncertainty. Besides, the input-output stability is proposed for discretizing the continuous-time controller of the fuzzy logic systems. Finally, computer simulation shows that the proposed method can easily reconstruct the continuous-time controller and has very good robustness for different sampling times.