Containment control for general discrete-time second-order multi-agent systems

The containment control problem for general discrete-time second-order multi-agent systems is investigated in this paper. Based on a distributed containment control algorithm with the state gain parameters in a given range, we transform the system to an equivalent error system, and then analyze the convergence of the error system by the eigenvalues of the corresponding coefficient matrix. Finally, a necessary and sufficient condition is derived to guarantee that all the followers asymptotically converge to a convex hull formed by the leaders and numerical examples are presented to demonstrate the validity of the theoretical findings.