Distributed ${\cal H}_{\infty}$ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks

Abstract

This paper is concerned with the distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of discrete-time Markovian jump nonlinear time-delay systems with deficient statistics of mode transitions. The system measurements are collected through a lossy sensor network subject to randomly occurring quantization errors and randomly occurring packet dropouts. The description of deficient statistics of mode transitions that account for known, unknown, and uncertain transition probabilities is comprehensive. A distributed filter design scheme is outlined by explicitly characterizing the filter gains in terms of some matrix inequalities. Simulation results demonstrate the effectiveness of the proposed filtering scheme.