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**Coordination of discrete-time multi-agent systems via relative output feedback.**
*(English)*
Zbl 1227.93013

Summary: This paper investigates the joint effects of agent dynamics and network topology on the consensusability of linear discrete-time multi-agent systems via relative output feedback. An observer-based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi-agent systems with discrete-time double integrator dynamics are discussed where a simple control protocol directly using two-step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation-based tracking problems. The theoretical results are illustrated by simulations.

### MSC:

93A14 | Decentralized systems |

93B52 | Feedback control |

94C15 | Applications of graph theory to circuits and networks |

### Keywords:

multi-agent systems; communication graphs; consensusability; eigenratio; formation-ability; leader-follower
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\textit{K. You} and \textit{L. Xie}, Int. J. Robust Nonlinear Control 21, No. 13, 1587--1605 (2011; Zbl 1227.93013)

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