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| On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks |
| TaoLiu1,JieHuang2,3 |
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| (1 Shenzhen Key Laboratory of Control Theory and Intelligent Systems, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China;2 Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen 518057, Guangdong, China
3 Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China) |
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| 摘要: |
| 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. |
| 关键词: Leader-following consensus · Exponential stabilization · Linear switched systems · Discrete-time systems |
| DOI：https://doi.org/10.1007/s11768-023-00168-5 |
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| 基金项目: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. |
|
| On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks |
| Tao Liu1,Jie Huang2,3 |
| (1 Shenzhen Key Laboratory of Control Theory and Intelligent Systems, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China;2 Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen 518057, Guangdong, China
3 Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China) |
| 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. |
| Key words: Leader-following consensus · Exponential stabilization · Linear switched systems · Discrete-time systems |
