$H_{\infty }$ Filtering For Nonlinear Discrete-Time Systems Subject to Quantization and Packet Dropouts

This paper investigates the problem of H_∞ filtering for a class of nonlinear discrete-time systems with measurement quantization and packet dropouts. Each output is transmitted via an independent communication channel, and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution, while the quantization errors are treated as sector-bound uncertainties. Based on a piecewise-Lyapunov function, an approach to the design of H_∞-piecewise filter is pro posed such that the filtering-error system is stochastically stable with a guaranteed H_∞ performance. Some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the Lyapunov matrices and the system matrices. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically tractable with commercially available software. Finally, two illustrative examples are provided to show the effectiveness of the proposed method.