Leader–follower consensus using 2-rate distributed output feedback protocol without controller interaction

This paper deals with the leader–follower consensus control for a homogeneous, discrete-time, multi-agent system (MAS) with agents having non-minimum phase (NMP) zeros. Linear time-invariant (LTI) or single-rate distributed output feedback schemes in which, the controllers are not allowed to exchange their states with the neighbours, may fail to achieve this objective, if a certain speed of consensus is needed. To remedy this, a 2-rate scheme is proposed in this paper. The lifting technique is used to transform the design of the proposed 2-rate distributed controller into the design of an equivalent LTI or single-rate centralized controller for an equivalent LTI plant, satisfying some complex gain margin (GM) criteria. It is shown that the inherent zero-placement capability of the proposed controller can make this equivalent LTI plant minimum phase under certain conditions, which helps one attain a desired speed of the consensus response while satisfying the GM criteria. An $H_{\infty }$/loop-transfer-recovery (LTR)-based approach is used to design the proposed controller. A suitable example is considered to show the efficacy of the proposed controller over its single-rate counterpart.