Fault detection for discrete-time Lipschitz nonlinear systems with signal-to-noise ratio constrained channels

In this paper, the problem of fault detection for discrete-time Lipschitz nonlinear systems with additive white Gaussian noise channels subject to signal-to-noise ratio constraints is investigated. An optimal residual generator based on the mixed H−/H∞H−/H∞ performance index is designed to generate the so-called residual signal, and the H−H−-index is used to measure the minimum effect of faults on the residual signal, while the influence of unknown disturbances and channel noise on the residual signal is maximized by the means of the H∞H∞-index. Then, in order to detect the occurrence of faults, a norm-based residual evaluation function is provided, and a dynamic threshold including upper bounds on the modulus of the solution of Lipschitz nonlinear systems and the stochastic properties of channel noise is also constructed. Finally, a simulated example is presented to demonstrate the effectiveness of the proposed approach.