Linear Programming-Based Fault Detection and Consensus Control of Positive Multi-agent Systems

This paper investigates the fault detection filter and consensus control of positive multi-agent systems with disturbances and faults. First, a kind of positive fault detection filter is designed by virtue of the positive system theory and filter design technology. Then, a fault detection filter-based consensus control protocol is proposed using relative state and output information of the agents. Under the designed fault detection filter and controller, sufficient conditions are presented to ensure the L − -gain performance and the hybrid L 1 -gain performance of the closed-loop systems in terms of linear programming. The positivity and consensus of multi-agent systems with disturbances and faults can be guaranteed by virtue of linear programming and co-positive Lyapunov function. The filter and control protocol gain matrices are determined by virtue of a matrix decomposition technique. Finally, one illustrative example is provided to verify the validity of the presented results.