Less conservative robust stabilization conditions for the uncertain polynomial fuzzy system under perfect and imperfect premise matching

By introducing some slack matrices, this paper proposes less conservative robust stabilization conditions for the polynomial fuzzy system with parametric uncertainties. In the proposed methods, no inverse polynomial matrices are chosen as the decision variables so that each element of the gain and the Lyapunov matrices can be guaranteed to strictly be a polynomial function. Therefore, the hardware implementation cost of operating the proposed controller is reduced because no rational functions need to be computed. Moreover, the fuzzy controllers are designed under perfect and imperfect premise matching conditions to enhance the design flexibility. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed methods.