Transfer function representation of cyclic consensus systems

Authors:
Myung-Gon Yoon;Koji Tsumura
Affiliations:
Department of Precision Mechanical Engineering, Gangneung-Wonju National University, Wonju, 220-711, Republic of Korea;Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper presents explicit forms of transfer functions for a class of cyclic consensus systems with different kinds of network topologies; directed, undirected and different numbers of reference agents. Each agent of consensus systems is assumed to satisfy a scalar integrator dynamics which is driven by a common consensus protocol and an independent exogenous input. It is shown that every single-input single-output (SISO) transfer function between the exogenous input of one agent and the state of another generally different agent, is always minimum phase. In addition, the poles and zeros, system degrees and relative degrees of those SISO transfer functions are specified. These results are interpreted in relation to the controllability and closed loop performance of a networked system with one leader agent. Furthermore, our transfer function representations are applied to an investigation of stability margins for a closed loop cyclic consensus system.