Distributed ${\cal H}_{\infty}$ Consensus of Higher Order Multiagent Systems With Switching Topologies

This brief addresses the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">${\cal H}_{\infty}$</tex-math></inline-formula> consensus problem of multiagent systems with higher order linear dynamics and switching directed topologies. Without assuming that the directed communication topology is fixed or balanced, a class of distributed protocols is constructed and employed to achieve state consensus while guaranteeing a prescribed disturbance rejection objective, with both admissible exogenous disturbances and unknown initial states. By using tools from algebraic graph theory and switched systems theory, it is proven that the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">${\cal H}_{\infty}$</tex-math></inline-formula> consensus in closed-loop multiagent systems with switching directed topologies can be achieved if the feedback gain matrix of the protocol is appropriately designed and the coupling strength among neighboring agents is larger than a derived positive value. Moreover, the consensus rate for the closed-loop nominal multi-agent systems is discussed.