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In this study, the existence of a common Lyapunov function to guarantee stability of a switching network of multi-agents with strongly connected unbalanced describing graphs and directional communication links is presented. The objective of the team is to achieve consensus while the team structure is arbitrarily changing during a given mission. Although the design strategy for the team of multi-agents is based on a semi-decentralised optimal control approach for the initial network topology, to guarantee consensus achievement for the switching network and for determining a common Lyapunov function for stability the optimal control gains have to be reassigned. It is shown that by introducing a criterion for selecting the control gains, desirable performance specifications for the switching network under the leader or the team topological changes can still be achieved.