Improved leaderless consenus criteria of networked multi-agent systems based on the sampled data

This paper is concerned with leaderless consensus of networked multi-agent systems with Lipschitz-type nonlinear dynamics based on the sampled data. By introducing a weighted average state of all nodes as the virtual leader, the error variables are defined as the distance between agents and the virtual leader. The improvements are done in two directions. First, several consensus conditions are derived by linear matrix inequalities based on Finsler's lemma instead of algebraic criteria based on the general algebraic connectivity. Finsler's lemma is utilised to deal with the linear dependence of the error variables. Second, a distributed event-triggered transmission strategy under the periodic sampling scheme is proposed to reduce the communication between agents and the control updates, which only need to check the event condition at each sampling instant, avoiding the continuous monitor. With the improved strategies, one theorem and two corollaries are derived and a co-design approach of the feedback gain and the event-triggered matrix is also presented. Finally, an example is provided to validate the effectiveness of the theoretical results.