Fault detection filter design with varying gains for multi-delay uncertain systems

The paper is concerned with the fault detection (FD) filter design problem in finite frequency domains for multi-delay systems subject to affine uncertainties. An adaptive mechanism is introduced to construct a new FD filter with varying gains, and the H∞ tracking method is used to generate the residual signal. By defining appropriate Lyapunov functional, the performance analysis is firstly conducted in finite frequency domains via Parseval׳s theorem. Subsequently, the FD filter design conditions are derived based on the result of performance analysis. Moreover, it is shown that, for the considered multi-delay uncertain systems, the FD filter with varying gains can achieve better FD performances than the existing ones with fixed gains. Finally, a numerical example is given to illustrate the advantages of the proposed theoretical result.