Robust H_∞ disturbance attenuation control of continuous-time polynomial fuzzy systems

This paper introduces a stabilization condition for polynomial fuzzy systems that guarantees H_∞ performance under the imperfect premise matching. An H_∞ control of polynomial fuzzy systems attenuates the effect of external disturbance. Under the imperfect premise matching, a polynomial fuzzy model and controller do not share the same membership functions. Therefore, a polynomial fuzzy controller has an enhanced design flexibility and inherent robustness to handle parameter uncertainties. In this paper, the stabilization conditions are derived from the polynomial Lyapunov function and numerically solved by the sum-of-squares (SOS) method. A simulation example and comparison of the performance are provided to verify the stability analysis results and demonstrate the effectiveness of the proposed stabilization conditions.