Stability and Control of Continuous TSK Fuzzy Systems

This paper introduces a new stability test and controller design methodology for Takagi-Sugeno-Kang (TSK) fuzzy systems. Unlike methods based on a common Lyapunov function, our stability results can be applied to systems with unstable consequents and our controllers can be designed for systems with unstabilizable consequents. Sufficient stability conditions are derived using the comparison principle and the Dini derivative. The stability results are used to design continuous-time fuzzy proportional controllers and fuzzy PI controllers. We provide examples to demonstrate our controller design. We show that our results compare favorably with results available in the literature and provide controllers where earlier approaches fail.