Novel framework on double event-triggered consensus of positive multi-agent systems

The paper investigates double adaptive event-triggered consensus (DAETC) for positive multi-agent systems (PMASs). The DAETC refers to the observer and control protocols. First, an adaptive event-triggered observer is constructed for the systems by designing an observer gain and the corresponding auxiliary gain. Then, an adaptive event-triggered consensus protocol is proposed based on the designed observer. Two kinds of adaptive event-triggered conditions are established for the observer and control protocols. Thus, a novel consensus framework is constructed in this paper for PMASs by introducing an additional term. Meanwhile, a double event-triggering mechanism is presented for PMASs. The gain matrices of the observer and control protocol are designed by means of linear programming (LP) and matrix decomposition techniques and some sufficient conditions are addressed to ensure positivity and consensus of the closed-loop systems. The contributions of the paper lie in that: (i) A novel DAETC framework is constructed, (ii) A tractable design approach is established to obtain the gains of observer and control protocols, and (iii) A simple analysis and computation approach containing co-positive Lyapunov function (CLF) and linear programming (LP) is presented for the systems. Finally, an example is given to verify the effectiveness of the theoretical results and the corresponding comparison simulations are provided by choosing different initial conditions. It is shown from these simulations that all states are driven to a non-negative region rather than zero and the sampling frequency of observer and the control protocol is reduced. A graphical abstract is shown.