Network‐based robust fault detection with incomplete measurements

Abstract

AbstractIn this paper, we deal with the robust fault detection problem for a class of discrete‐time networked systems with unknown inputs. Three types of incomplete measurements frequently occurred in a network environment are simultaneously considered, which include (1) measurements with communication delays, (2) measurements with packet dropouts, and (3) measurements with signal quantization. A unified measurement model utilizing a set of Kronecker delta functions is proposed to describe the delay and missing phenomenon, and the quantization is assumed to be of the logarithmic type. Attention is focused on the analysis and design of a robust full‐order fault detection filter such that, for all admissible unknown inputs and incomplete measurements, the error between residual and fault is kept as small as possible. By augmenting the states of the original system and the fault detection filter, the addressed robust fault detection problem is converted into an auxiliary robust H∞ filtering problem. Parameter‐dependent and delay‐probability‐dependent approaches are developed in the design process in order to have a less conservative result. Sufficient conditions for the existence of the desired robust fault detection filters are established in terms of certain linear matrix inequalities (LMIs), and explicit parameters of the desired filter are then characterized if these LMIs are feasible. A numerical example is provided to illustrate the applicability of the proposed technique. Copyright © 2008 John Wiley & Sons, Ltd.