New Result on Mismatched Double Fuzzy Summation Inequality

This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.