LP-based Positive Leader-following Consensus Protocol for PMASs Under Sensor and Actuator Faults*

To address the challenges posed by sensor faults (SFs), actuator faults (AFs), and external disturbances, this paper introduces a positive leader-following consensus protocol (PLFCP) for positive multi-agent systems, aiming to prevent anomalous operations and system failures. We provide a novel PLFCP for PMASs under SFs using relative output information and states of the leader and followers. The positivity and leader-following consensus of PMASs can be guaranteed in terms of positive systems theory and co-positive Lyapunov function (CPLF). In addition, a linear programming (LP) is presented to obtain the corresponding positivity and consensus conditions. In the presence of SFs and external disturbances, we propose a matrix decomposition-based approach to construct a PLFCP with ${\mathcal{L}}_{1}$-gain performance, specifically designed for addressing SFs and AFs in positive multi-agent systems. Finally, an illustrative example is provided to verify the validity of the obtained results.