Abstract This paper investigates the nonfragile H ∞ filtering problem for a class of discrete-time nonlinear switched systems with quantization. The nonlinearity considered in our work is assumed to satisfy the Lipschitz conditions. The asynchronous switching is taken into consideration in the filter design. To study the asynchronous switching, a lag is introduced between the switching of subsystem and its matched filter. The Lyapunov functions are allowed to increase during the running time of activated subsystem with its mismatched filter. Both the measurement output signal and the performance output signal are quantized by two static quantizers before being transmitted, respectively. This consideration of quantization is more practical than the case that the signal quantization only exists in the measurement output signal. The main attention of this paper is to design a set of mode-dependent nonfragile H ∞ filters such that the filtering error systems are globally uniformly asymptotically stable and satisfy a weighted H ∞ performance index. Based on the average dwell time approach and multiple Lyapunov functions, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The desired nonfragile H ∞ filters can be obtained by solving these LMIs. Finally, an example is provided to illustrate the effectiveness of the obtained results.

中文翻译：

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具有量化的离散时间非线性切换系统的异步非脆弱 H∞ 滤波

摘要 本文研究了一类具有量化的离散时间非线性切换系统的非脆弱H ∞ 滤波问题。我们工作中考虑的非线性假设满足 Lipschitz 条件。在滤波器设计中考虑了异步切换。为了研究异步切换，在子系统切换与其匹配滤波器之间引入了滞后。Lyapunov 函数允许在激活子系统的运行时间内增加其失配滤波器。测量输出信号和性能输出信号在传输前分别由两个静态量化器进行量化。这种量化的考虑比信号量化仅存在于测量输出信号中的情况更实用。本文的主要关注点是设计一组与模式相关的非脆弱 H ∞ 滤波器，使得滤波误差系统全局一致渐近稳定并满足加权 H ∞ 性能指标。基于平均停留时间方法和多个李雅普诺夫函数，以线性矩阵不等式（LMI）的形式建立充分条件。可以通过求解这些 LMI 来获得所需的非脆弱 H ∞ 滤波器。最后给出一个例子来说明所得结果的有效性。以线性矩阵不等式 (LMI) 的形式建立充分条件。可以通过求解这些 LMI 来获得所需的非脆弱 H ∞ 滤波器。最后给出一个例子来说明所得结果的有效性。以线性矩阵不等式 (LMI) 的形式建立充分条件。可以通过求解这些 LMI 来获得所需的非脆弱 H ∞ 滤波器。最后给出一个例子来说明所得结果的有效性。