Fault Detection Filter Design for Switched Positive Systems Under Deception Attack

We investigate the fault detection problem for switched positive systems under deception attack in this article. The deception attack is modeled as a nonlinear function obeying Bernoulli distribution, which will bring additional difficulty to detect random occurring fault. A filtering system is constructed as a residual generator to detect the fault with considering deception attack. Then, by applying copositive Lyapunov-Krasovskii function theory, sufficient condition for stability with
$L_{1}$
-gain and
$L$
-gain performances are presented, respectively. Subsequently, coefficient matrices of fault detection filter are presented to detect fault with the robustness of disturbance and the sensitiveness of fault. Finally, a numerical example verifies the validity of the method.