Multi-consensus of multi-agent networks via a rectangular impulsive approach

A multi-consensus problem is studied in multi-agent networks. The interaction mechanism of competition/abstention/cooperation among agents is introduced. Three rectangular impulsive protocols are proposed to solve multi-consensus of second order multi-agent networks with a directed topology. These algorithms have the performance of Dirac impulsive control and discrete-time control. Necessary and sufficient conditions are obtained for the stationary multi-consensus and the dynamic multi-consensus. Numerical examples are provided to illustrate the effectiveness of the obtained criteria.