Distributed fault estimation basing on a united adaptive and sliding-mode observer for multi-agent systems

In this technical note, under the undirected communication topology, a united adaptive and sliding-mode observer is designed to detect and estimate the actuator faults with the use of a linear matrix inequality (LMI) for multi-agent systems. Firstly, for each agent, the system is decoupled into two subsystems through matrix transformation so that the faults are isolated from disturbances. On the one hand, the adaptive observer is designed to estimate the faults for the subsystem without disturbances. On the other hand, the sliding-mode observer is put forward for the subsystem with disturbances to guarantee the robustness against the disturbances. Then, from an overall perspective, the whole error dynamics is obtained by defining global error vectors. Furthermore, the proposed design can be represented with LMIs to establish a systematic design procedure and can be proved by Lyapunov stability theory. Finally, simulation results are shown to demonstrate the effectiveness of the proposed design technique.