Fault Detection for Linear Discrete Time-Varying Systems Subject to Random Sensor Delay: A Riccati Equation Approach

This paper mainly studies the fault detection (FD) problem for linear discrete time-varying systems subject to random sensor delay. By assuming that the measurement channel is with Transmission Control Protocol (TCP), an observer-based FD filter (FDF) is provided as a residual generator via embedding the packet indicator into the filter. To construct this FDF, its design issue is formulated into two sub-problems. One is to maximize the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_{-}/\mathcal {H}_{\infty }$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }/\mathcal {H}_{\infty }$ </tex-math></inline-formula> FD performance index, which aims to enhance the ratio of fault sensitivity/disturbance attenuation. The other one is to find the filter parameter matrices such that the error between the residual and the fault is minimized in the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> sense. By employing stochastic analysis and introducing some adjoint operator based optimization approaches, analytical solutions to the aforementioned FDF design problem are derived via solving recursive Riccati equations. An illustrative example is given to show the effectiveness of the proposed methodologies.