Event-triggered H–/L∞ fault detection observer design for discrete-time Lipschitz nonlinear networked control systems in finite-frequency domain

This paper proposes an event-triggered $ H_{\_}/L_{\infty } $ H−/L∞ fault detection observer (FDO) design method for discrete-time Lipschitz nonlinear networked control systems (NCSs) in finite-frequency domain. First, a discrete event-triggered transmission scheme is proposed to mitigate the utility of limited network bandwidth. Second, with the aid of a reformulated Lipschitz property, the nonlinear error dynamics are converted into a linear parameter varying (LPV) networked system model. Third, based on this model, the finite-frequency $ H_{\_} $ H_/L∞ index is used to measure the worst-case fault sensitivity performance and the $ L_{\infty } $ H_ norm from unknown disturbance to residual is used to measure disturbance robustness performance. Next, a residual evaluation and a dynamic threshold are synthesised based on the $ L_{\infty } $ L∞ norm. Furthermore, sufficient conditions of the FDO design are derived and transformed by a set of linear matrix inequalities (LMIs). The proposed FDO design method can significantly reduce the data transmission to relieve the communication pressure, and can also achieve better FD performance than the full frequency domain. Finally, A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.