Guaranteed cost consensus problems for second-order multi-agent systems

Guaranteed cost consensus for second-order multi-agent systems with fixed topologies are investigated. Firstly, a cost function is constructed based on state errors among neighbouring agents and control inputs of all the agents, which is to find a tradeoff between the consensus regulation performance and the control energy consumption. Secondly, by the state-space decomposition approach and the Lyapunov method, a sufficient condition for the guaranteed cost consensus is presented and an upper bound of the cost function is given. It should be pointed out that these criteria are related to the second smallest and the maximum eigenvalues of the Laplacian matrix associated with the interaction topology. Thirdly, an approach is presented to obtain the consensus function when second-order multi-agent systems achieve guaranteed cost consensus. Finally, numerical simulations are given to demonstrate theoretical results.