Fault Detection for a Class of Nonlinear Singular Systems Over Networks with Mode-Dependent Time Delays

In this paper, the fault detection problem is investigated for a class of nonlinear discrete-time singular systems over networks with mode-dependent time delays. The transmission delays are modeled as a Markov chain with partly known distribution, which takes values in a finite state space. By augmenting the original nonlinear singular system and the fault detection filter, the resulting fault detection dynamics is formulated as an $$H_{\infty }$$H∞ filtering problem of a singular Markov jump system. Regular, casual, stochastically stable of the fault detection dynamics and the prescribed $$H_{\infty }$$H∞ attenuation level are obtained by the mode-dependent Lyapunov functional approach. The desired fault detection filter is obtained in terms of a series of feasible LMIs. A numerical example is presented to show the effectiveness of the developed technique.