Finite-time $H_{-}/H_{\infty}$ Fault Detection for Singular systems with Time-varying Delay

In this paper, the finite time
$H_{-}/H_{\infty}$
fault detection(FD) problem for linear singular systems with time-varying delays is studied. Firstly, based on the L-K functional method and some algebraic techniques, sufficient conditions are given for the system which is regular, impulse-free and finite time stable satisfies the
$H_{\infty}$
performance and the
$H$
- performance, respectively. Then, the design conditions of FD filter with disturbance attenuation performance and fault sensitivity performance are given, respectively. After that, an optimization algorithm is given to achieve the balance between the two indexes and solve the best FD filter. Finally, a numerical example is given to verify the validity of the proposed method.