Containment control of discrete-time multi-agent systems based on delayed neighbours' information

This paper considers the containment control problem for multi-agent systems with multiple leaders. A distributed control protocol is designed so that the states of the followers converge to the smallest convex hull containing the states of all the leaders. The result is extended to the moving leaders case. Two level protocols are provided such that the leaders can achieve a formation while the followers converge into the convex hull formed by the leaders. The control protocols are based on neighbours' control inputs. A sufficient condition on the control gain is provided to guarantee the convergence. A numerical example is given to demonstrate the result.