H∞ filter design for fuzzy systems with quantized measurements

This paper addresses the problem of H∞H∞ filtering for a class of discrete time T–S model based fuzzy systems with quantized measurements. The measurement signal is quantized by a logarithmic quantizer. By using basis dependent Lyapunov function, a sufficient condition is provided to ensure the stability of the filtering error system and to guarantee a given H∞H∞ performance level. Based on this analysis result of the filtering error system, an explicit filter design approach is proposed and the basis dependent filtering algorithm is further improved by using a kind of relaxed technique. Two numerical examples are also presented to show that the filtering algorithm based on the basis dependent Lyapunov function has less conservative than the one based on the basis independent Lyapunov function.