Fault detection for a class of non-linear networked systems with Markovian transmission delays

Abstract

In this paper, we investigate the fault detection problem for a class of discrete-time non-linear networked systems with Markovian network-induced delays. It is assumed that networks exist in both communication channels from the sensor to the controller and from the controller to the actuator. The transmission delays of sensor-to-controller and controller-to-actuator are modelled as two homogeneous Markov chains, which takes values in finite state spaces, respectively. Then, we focus on the design of a full-order fault detection filter (FDF) such that the system performance index is still achieved in spite of the fault. By augmenting the states of the original system and the FDF, the fault detection problem is transformed into an auxiliary H∞ filtering problem of a certain Markovian jump system. A sufficient condition for the existence of the desired filter is established in terms of a series of linear matrix inequalities (LMIs). The explicit parameters of the desired filter are determined if these LMIs are feasible. Two numerical examples are provided to show the effectiveness and applicability of the proposed method.