Fault detection over noisy wireless channels

In this paper, the fault detection problem over a noisy wireless channel is studied. The presence of bit errors in data transmission can degrade the fault detection performance. The reliability of the network is a critical issue for the system design. We first analyze the characteristics of the communication over a noisy channel from the view of coding theory, and obtain the bounds of the transmission errors due to bit errors in different positions of a binary information sequence. Those bounds are then reconstructed as the system uncertainties. Based on the result, we formulate the fault detection system as a Markov jumping linear system (MJLS), and solve the H_infin optimal problem for the threshold calculation with the help of the linear matrix inequality (LMI) technique.