Necessary and Sufficient Conditions for Consensus of Second-Order Multiagent Systems Under Directed Topologies Without Global Gain Dependency

The consensus problem for second-order multiagent systems with absolute velocity damping under directed topologies is investigated. In contrast to the existing results, which rely on a sufficiently large common absolute velocity damping gain above a lower bound dependent on global information, this paper focuses on novel algorithms to overcome this limitation. A novel consensus algorithm, where different agents use different absolute velocity damping gains, is first proposed. In the absence of delays, based on a system transformation method, the consensus problem for second-order multiagent systems is converted into that for first-order multiagent systems with the agent number doubled. Necessary and sufficient conditions are then derived under directed topologies by relating the topologies associated with the doubled number of agents and the original team of agents. In the presence of multiple constant delays, based on a further system transformation method, the consensus problem for second-order multiagent systems is converted into the stability problem for corresponding systems. Necessary and sufficient conditions are presented to guarantee consensus under a directed fixed topology. For systems with a uniform constant delay, more concrete necessary and sufficient conditions on how large the delay can be to guarantee consensus is given. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.