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On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks

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Abstract

The leader-following asymptotic consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks was solved about a decade ago. Recently, the leader-following exponential consensus was further established using the so-called Krasovskii–LaSalle theorem for a class of discrete-time linear switched systems. But this method involves some advanced concepts such as the weak zero-state detectability of some limiting system. In this paper, we offer a simpler solution to the leader-following exponential consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks. After converting the solvability of the problem to the establishment of the exponential stability for a class of discrete-time linear switched systems, we first show that this class of linear switched systems is uniformly completely observable. Then, we further conclude that the uniform complete observability for this class of linear switched systems implies the exponential stability for the same class of linear switched systems, thus leading to the solution of the leader-following exponential consensus problem. Moreover, our approach also gives rise to an explicit characterization of the exponential convergence rate of the leader-following consensus problem.

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Authors and Affiliations

  1. Shenzhen Key Laboratory of Control Theory and Intelligent Systems, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, China

    Tao Liu

  2. Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen, 518057, Guangdong, China

    Jie Huang

  3. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China

    Jie Huang

Authors
  1. Tao Liu
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  2. Jie Huang
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Correspondence to Jie Huang.

Additional information

This work was supported in part by the Shenzhen Key Laboratory of Control Theory and Intelligent Systems under Grant No. ZDSYS20220330161800001, in part by the Research Grants Council of the Hong Kong Special Administrative Region under Grant No. 14201420, and in part by the National Natural Science Foundation of China under Grant No. 61973260.

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Liu, T., Huang, J. On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks. Control Theory Technol. 21, 469–477 (2023). https://doi.org/10.1007/s11768-023-00168-5

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  • DOI: https://doi.org/10.1007/s11768-023-00168-5

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