An H∞ consensus achievement for LTI multi-agent systems with directed fixed networks

The H
_∞
consensus problem of homogeneous linear time invariant (LTI) multi-agent systems with a fixed directed communication network graph is studied in this paper. A design technique is proposed based on the solution of an algebraic Riccati equation without the need to solve linear matrix inequalities (LMIs). The design procedure is in two steps. First agents are made marginally stable by using a local state feedback controller. In the second step, a relative state feedback controller is designed to achieve consensus. It is worth mentioning that these steps can be performed independently. The stability of the proposed controller is investigated based on Lyapunov stability analysis. The effectiveness of the proposed consensus algorithm is illustrated through numerical simulations.