Fault detection for a class of uncertain Lipschitz systems with time delays in finite‐frequency domain

Abstract

This study investigates the problem of fault detection (FD) filter design for a class of uncertain Lipschitz systems with time delays, unknown faults, parameter uncertainties and bounded disturbances. A novel FD filter is proposed and the augmented filter system is converted to a linear parameter varying (LPV) system by the reformulated Lipschitz property. Then, two bounded real lemmas (BRLs) are given for the generated residual signal to achieve the fault sensitivity performance in low-/middle-/high-frequency domains and disturbance attenuation performance in the full-frequency domain. Next, the obtained BRLs are further converted into a set of linear matrix inequalities (LMIs) to implement the filter design. Finally, two illustrative simulations including a numerical example and Chua's circuit system clearly demonstrate the advantages of the developed FD scheme.