Observer-based fixed-time consensus tracking for second-order multi-agent systems with disturbances

This paper researches into a fixed-time consensus tracking problem for a class of second-order multi-agent systems (MASs) subject to external disturbances based on a fixed-time observer. First, we adopt a state observer to change the states of each agent from unknown to known. The observer is designed so that observed states and the leader's state reach consensus. Second, according to the designed controller, states of each agent and observed states achieve consensus, namely leader-following consensus is realized and the setting time of which is obtained without depending on initial states. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve fixed-time consensus tracking for second-order MASs with disturbances. Finally, the validity of the design is verified by numerical arithmetic examples.