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Synchronization of discrete-time multi-agent systems on graphs using H2-Riccati design

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4 Author(s)
Hengster-Movric, K. ; Autom. & Robot. Res. Inst., Univ. of Texas at Arlington, Fort Worth, TX, USA ; Keyou You ; Lewis, F.L. ; Lihua Xie

In this paper design methods are given for synchronization control of discrete-time multi-agent systems on directed communication graphs. The graph properties complicate the design of synchronization controllers due to the interplay between the eigenvalues of the graph Laplacian matrix and the required stabilizing gains. A method is given herein, based on an H2 type Riccati equation, that decouples the design of the synchronizing gains from the detailed graph properties. A condition for synchronization is given based on the relation of the graph eigenvalues to a bounded circular region in the complex plane that depends on the agent dynamics and the Riccati solution. This condition relates the Mahler measure of the node dynamics system matrix to the connectivity properties of the communication graph. The notion of `synchronizing region' is used. An example shows the effectiveness of these design methods for achieving synchronization in cooperative discrete-time systems.

Published in:

Control Applications (CCA), 2012 IEEE International Conference on

Date of Conference:

3-5 Oct. 2012

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