A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations

In this paper, the problem of robust fault detection filter (RFDF) design for a class of linear systems with some nonlinear perturbations and mixed neutral and discrete time-varying delays is investigated. By using a descriptor technique, 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 the 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 numerical example is provided to demonstrate the effectiveness and the applicability of the proposed method.