Exponential synchronisation of nonlinear multi-agent systems via distributed self-triggered hybrid control with virtual linked agents

In this paper, exponential synchronisation of nonlinear multi-agent systems with K agents by distributed self-triggered hybrid control and virtual link mechanism is investigated. Based on the Lyapunov function and linear matrix inequalities, some synchronisation conditions are provided. Because of using the virtual link, the system can be divided into two subsystems, real link subsystem and virtual link subsystem. They can be synchronised with the desired dynamical behaviours by using the same self-triggered hybrid control. Hence, the original dimension (K) of synchronisation conditions can be reduced to [K/2] (K/2 round up). Finally, a simulation example is given to demonstrate the performance of the proposed approaches.