Leader-following consensus of second-order multi-agent systems: new results based on linear transformation method

This paper discusses the leader-following consensus problem of second-order homogeneous multi-agents systems, in which it takes into consideration some different cases about the parameter in position difference and velocity difference. Firstly, we use the incidence matrix of the directed spanning tree to construct a linear transformation matrix, and the consensus problem is equivalently converted into the stability problem concerning input to the state.When there are no constraint on the control parameters, through Lyapunov stability and the linear matrix inequality, we can get better control parameters to make the system asymptotically reach the state consensus and ensure the convergence rate of the system. We analyzed three special cases and compared the previous results. We use the condition that the real part of the eigenvalue of matrix equivalent to A̅ is less than zero when the matrix is Hurwitz stable. This way can calculate a broader set of values of the control parameters more simply and clearly. Finally, numerical examples are presented to validate the theoretical results.