Semi-global Consensus of Multi-agent Systems with Impulsive Approach

  • Zhen LiEmail author
  • Jian-an Fang
  • Tingwen Huang
  • Wenqing Wang
  • Wenbing Zhang
Living reference work entry


Consensus analysis is a basic issue of multi-agent systems. As an important topic of this issue, semi-global consensus problems have aroused interests since the capability of actuator is usually limited in the presence of a finite range in practice. In theory, semi-global consensus problems refer to design a one-parameter family of control protocols whose domain of attraction can tend to the entire state space. To deal with these problems, the low-gain feedback control strategy has been recently extended. The presented chapter offers a short survey of current studies on this topic, and then we develop the basic idea of low-gain feedback control strategy to apply a distributed impulsive strategy. Similarly with the low-gain feedback control, the magnitude of the proposed impulsive protocol can converge to zero as the low-gain parameter tends to zero. By utilizing the Lyapunov function and low-gain theory, a parametric discrete-time Riccati equation is developed for calculating control gain matrix. Then, based on low-and-high-gain feedback control, another distributed impulsive strategy is considered such that this control protocol can be limited in a finite range. Furthermore, two algorithms are proposed to solve the corresponding the control gain matrices. Subsequently, future research topics are discussed.


Multi-agent systems Semi-global consensus Low-gain feedback control Impulsive approach 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Zhen Li
    • 1
    Email author
  • Jian-an Fang
    • 2
  • Tingwen Huang
    • 3
  • Wenqing Wang
    • 1
  • Wenbing Zhang
    • 4
  1. 1.School of AutomationXi-an University of Posts & TelecommunicationsXi-anChina
  2. 2.School of Information Science and TechnologyDonghua UniversityShanghaiChina
  3. 3.The Science ProgramTexas A&M UniversityDohaQatar
  4. 4.Department of MathematicsYangzhou UniversityJiangsuChina

Section editors and affiliations

  • Yang Tang
    • 1
  1. 1.Department of AutomationEast China University of Science and TechnologyShanghaiChina

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