Consensus of multi-agent systems with unbalanced topology

Multi-agent systems with balanced topology have been considered intensively in the existing literature. This paper studies consensus of multi-agent systems with unbalanced topology. Two consensus protocols are proposed to solve consensus problems. A novel disagreement function is presented for convergence analysis of consensus protocols. Sufficient conditions for consensus of multi-agent systems are established in both cases. An important finding is that the spanning directed tree plays a key role in addressing consensus. The jointly spanning directed tree is introduced for convergence analysis of multi-agent systems with switching topologies. Simulations are given for illustration the effectiveness of the proposed consensus protocols.