Distributed ${\mathcal{H}}_{\infty}$ Filtering for a Class of Discrete-Time Markov Jump Lur’e Systems With Redundant Channels

Abstract

This paper investigates the problem of distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for a class of discrete-time Markov jump Lur'e systems over sensor networks with stochastic switching topologies. As a first effort, the redundant channels are considered to use in the data transmission to strive against the fragility of networks commonly configured by a single channel in the communication networks subject to quantization and randomly occurring packet dropouts. By constructing a Lur'e-type Lyapunov function interconnected with a cone-bounded nonlinearity, the filtering performance analysis for the underlying systems is carried out first. Then, a new class of distributed filters, which can be used to reflect the mismatching characteristic of modes jumping between the target plants and the proposed filters, is designed such that the filtering error system is stochastically stable and achieves a prescribed average H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index. A numerical example is provided to show the effectiveness of the proposed filtering scheme.