Consensus tracking of linear multi-agent systems under networked observability conditions

This paper addresses the consensus tracking problem for both continuous- and discrete-time linear multi-agent systems with a dynamic leader under networked observability conditions. Among followers, the communication topology is assumed to be undirected and connected. Two networked observability conditions are introduced and discussed. The first one extends the traditional detectability condition for a single system, while the second one is a full rank condition, which is stronger than the first one. In the continuous-time case, two distributed observer-based protocols are designed under corresponding networked observability conditions, respectively. Specifically, the second protocol is an adaptive one, which has a better robustness performance than the first one. In the discrete-time case, a distributed observer-based protocol is presented under the full rank networked observability condition. It is found that under the networked observability conditions, consensus tracking can still be achieved even if there exists no follower being able to track the leader independently. Based on algebraic graph theory and Lyapunov stability theory, some sufficient conditions are derived for reaching consensus tracking. Finally, simulation examples are presented to verify the effectiveness of theoretical results.