Unknown input observer based distributed fault detection for nonlinear multi-agent systems with probabilistic time delay

This paper focuses on the fault detection (FD) problem for nonlinear continuous-time multi-agent systems (MASs) with external disturbances and random time-varying delay. The communication topology is assumed to be undirected and connected. Firstly, a stochastic variable satisfying the Bernoulli distribution is utilized to describe the random time-varying delay and transfer the random time-varying delay to a deterministic time-varying delay. To avoid the constraints of the rank conditions for unknown input observer (UIO), the external disturbances and faults from other agents are treated as the unknown inputs which are partitioned into the decoupled part and the non-decoupled part. Sufficient conditions composed of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the augmented system with a desired H∞ performance index and extra freedom of design. By utilizing the properties of UIOs properly, the method proposed in this paper can detect multiple faulty nodes simultaneously. Finally, a numerical example demonstrates the effectiveness and feasibility of the proposed approach.