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

  • Authors:

  • Kristian Hengster-Movric;Keyou You;Frank L. Lewis;Lihua Xie

  • Affiliations:

  • UTARI, University of Texas at Arlington Research Institute, 7300 Jack Newell Blvd. S, Ft. Worth, TX 76118, USA;Department of Automation, Tsinghua University, Beijing, 100084, China;UTARI, University of Texas at Arlington Research Institute, 7300 Jack Newell Blvd. S, Ft. Worth, TX 76118, USA;EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore, 639798, Singapore

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2013

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Abstract

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. Two methods are given herein that decouple the design of the synchronizing gains from the detailed graph properties. Both are based on computation of the local control gains using Riccati design; the first is based on an H"~ type Riccati inequality and the second on an H"2 type Riccati equation. Conditions are given for synchronization 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. The notion of 'synchronizing region' is used. An example shows the effectiveness of these design methods for guaranteeing synchronization in cooperative discrete-time systems.