Fault Detection for Semi-Markov Switching Systems in the Presence of Positivity Constraints

The fault detection issue is investigated for complex stochastic delayed systems in the presence of positivity constraints and semi-Markov switching parameters. By choosing a mode-dependent fault detection filter (FDF) as a residual generator, the corresponding fault detection is formulated as a positive
$\mathscr {L}_{1}$
filter problem. Attention is focused on the design of a mode-dependent FDF to minimize the error between the residual signal and the fault signal. The designed FDF features good sensitivity of the faults and robustness against the external disturbances. Subsequently, by means of the linear copositive Lyapunov functional (LCLF), stochastic stability is proposed to satisfy an expected
$\mathscr {L}_{1}$
-gain performance. Some solvability conditions for the desired mode-dependent FDF are established with the help of a linear programming approach. Finally, an application example of a data communication network model is provided to demonstrate the effectiveness of the theoretical findings.