Leader-following consensus of networked second-order agents with delayed information transmission

In this study, distributed leader-following consensus for a class of second-order multi-agent systems with delayed information transmission is studied. Based on and only on the relative delayed information between neighbouring agents, two distributed consensus protocols are designed and analysed. The first one is adopted to achieve leader-following consensus for the case where both relative delayed position and velocity measurements are available for neighbouring agents. For the second case where only the relative delayed position measurements can be used for coordination, a new type of observer-based protocol is constructed. By using tools from frequency domain analysis and control theory, several necessary and sufficient conditions for the existence of such protocols under a directed communication topology are established. Finally, simulation examples are performed to verify the theoretical analysis.