Linear Programming-Based Consensus of Positive Continuous-Time Multi-Agent Systems

Dear Editor, This letter deals with the consensus of positive multi-agent systems (PMASs). A consensus protocol is proposed by introducing a finite consensus point. An error is defined as the differences in the linear combination of the agent states, the agent states, and the finite consensus point. Under the consensus protocol, an error system is constructed, and it refers to the error term and the finite consensus point. A linear programming (LP)-based equation is given to remove the dependence of the finite consensus point. By virtue of the property of a directed graph, an error-independent system is obtained. A copositive Lyapunov function (CLF) is used to derive the consensus of the systems.