Fuzzy Generalized <inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_{2}$ </tex-math> </inline-formula> Filtering for Nonlinear Discrete-Time Systems With Measurement Quantization

Abstract

In this paper, the generalized ${\mathcal {H}_{2}}$ filter design problems are addressed for a class of nonlinear discrete-time systems with measurement quantization. The considered nonlinear system is represented by Takagi–Sugeno fuzzy model and the system measurement output is quantized by a dynamic quantizer constituted by a static quantizer and a dynamic parameter before it is transmitted to the filter. The attention is focused on the design of both full- and reduced-order filters and the quantizer dynamic parameter such that the quantized filtering error systems are asymptotically stable with prescribed generalized ${\mathcal {H}_{2}}$ performances. Superior to existing results on the quantized filtering design, the proposed one is given under a unified linear matrix inequality (LMI) characterization, it is shown that the design problem can be solved if the LMIs conditions are feasible. Finally, simulation examples will be exploited to illustrate the effectiveness of the developed quantized generalized ${\mathcal {H}_{2}}$ filtering methods.