In this study, the existence of a common Lyapunov function to guarantee stability of a switching network of multiagents 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.