Robust fault detection filter design for a class of linear systems with mixed time-varying delays and nonlinear perturbations

In this note, the problem of robust fault detection filter (RFDF) design for a class of linear systems subjected to some nonlinear perturbations and mixed neutral and discrete time-varying delays is investigated based on an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> performance condition. By introducing a descriptor technique, using Lyapunov-Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Based on Luenberger type observers, the explicit expression of the filters is derived for the fault such that both asymptotic stability and a prescribed level of disturbance attenuation are satisfied for all admissible nonlinear perturbations. A numerically example is provided to show performance of the proposed design approach.