Guaranteed Cost Consensus for Second-order Leader-following Multi-agent Systems with Time Delays

The current paper is concerned with guaranteed cost consensus control for second-order multi-agent systems with time-invariant delays. First, based on the state errors, the guaranteed cost consensus control protocol is proposed, where the impacts of the time delays can be dealt with and the tradeoff between the consensus regulation performance and the control energy consumption can be realized. Then, sufficient criteria for the guaranteed cost consensus are derived, where the dimension of matrix variables is not dependent on the number of agents, and an approach to determine a guaranteed cost value is presented, which associates with the initial state errors and the delay term. Finally, numerical simulation examples are shown to demonstrate the theoretical results.