New approach to H ∞  filtering of two-dimensional T-S fuzzy systems



This paper is concerned with the H ∞  filtering problem for two-dimensional T-S fuzzy systems. Sufficient conditions for the solvability of this problem are obtained by using basis-dependent Lyapunov functions. By considering the measured output as an independent variable with respect to the state variable and the disturbance input, a new method for designing two-dimensional H ∞  filters is presented. Moreover, it has been shown that the proposed method is equivalent to the conventional one. Therefore, the proposed method does not lead to any conservativeness that may be caused by separately considering the measured output, the state variable, and the disturbance input. In converting the parameterized linear matrix inequalities (PLMI) into LMI constraints, attention is focused on the reduction of the number of LMI-based conditions. On the basis of the proposed theorem, the number of LMI-based conditions is reduced to r3 from r3(r + 1)2 ∕ 4 by the conventional method. Thus, the computational advantage is obvious for fuzzy systems with large number of fuzzy rules. Simulation results have demonstrated the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.