Couple-group \(\mathcal{L}_2-\mathcal{L}_\infty\) Consensus of Nonlinear Multi-agent Systems with Markovian Switching Topologies

  • Xiao Li
  • Cancan Zhou
  • Jianping ZhouEmail author
  • Zhen Wang
  • Jianwei Xia


The paper is devoted to the couple-group \(\mathcal{L}_2-\mathcal{L}_\infty\) consensus problem of nonlinear multi-agent systems affected by external disturbances. The interaction topologies among agents obey a continuous-time Markovian process with unknown transition probabilities. By a system transformation, the problem of couple-group \(\mathcal{L}_2-\mathcal{L}_\infty\) consensus is converted into a \(\mathcal{L}_2-\mathcal{L}_\infty\) control issue. Then, by Lyapunov stability theory and graph theory, sufficient conditions for the couple-group \(\mathcal{L}_2-\mathcal{L}_\infty\) consensus are obtained. The control gains can be acquired via the solutions of a group of linear matrix inequalities. Moreover, the present method is extended to the multi-group \(\mathcal{L}_2-\mathcal{L}_\infty\) consensus. Finally, an example is provided to illustrate the effectiveness of the results.


Couple-group consensus \(\mathcal{L}_2-\mathcal{L}_\infty\) control multi-agent system Markovian switching 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xiao Li
    • 1
    • 2
  • Cancan Zhou
    • 2
  • Jianping Zhou
    • 2
    Email author
  • Zhen Wang
    • 3
  • Jianwei Xia
    • 4
  1. 1.School of Computer Science and TechnologyHuaibei Normal UniversityHuaibeiChina
  2. 2.School of Computer Science and TechnologyAnhui University of TechnologyMa’anshanChina
  3. 3.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  4. 4.School of Mathematics ScienceLiaocheng UniversityLiaochengChina

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