Distributed event-triggered positive consensus protocol design for leader-following multi-agent systems

In this paper, the event-triggered leader-following positive consensus (LFPC) problem of multi-agent systems (MASs) is studied. Through the application of positive system theory, a sufficient and necessary condition is established to ascertain that the obtained closed-loop system qualifies as a positive system. Next, by creating the consensus error system and applying an appropriate copositive Lyapunov function, the paper presents a sufficient condition for achieving LFPC. As a result, the matrix decomposition method is applied to matrix K, and a feasible design scheme for a distributed consensus protocol is presented in a solvable linear programming (LP) format to accomplish LFPC. In contrast to conventional approaches based on linear matrix inequalitie (LMI), the proposed distributed protocol scheme utilizing LP presents a more straightforward set of consensus conditions and reduces computational complexity. This simplification facilitates the management of large-scale MASs. To illustrate the efficacy of the developed distributed event-triggered positive consensus protocol, one example is provided within the framework of communication networks.