Output feedback control of mixed H₂/H_∞ multi-agent consensus via an inner auxiliary system approach

This paper investigates the mixed H₂/H_∞ consensus control problem for linear multi-agent systems subject to two types of disturbances. For multi-agent systems with undirected graph, the full control and standard output feedback control are considered, respectively. To this end, inner auxiliary systems are constructed for the transformed subsystems, based on which consensus conditions are derived in terms of linear matrix inequalities with an algebraic Riccati equation. It is shown that designed protocols not only can guarantee consensus with prescribed mixed H₂/H_∞ performance, but also result in a similar separation property as in the design of the controllers of single linear systems. Moreover, we extend the inner auxiliary system approach and the separation property to the directed graph case. Finally, some numerical examples are presented to illustrate the effectiveness of the theoretical results.