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vian switching and the Markov chain theory, we have established the necessary and sufficient conditions for
achieving the cooperatability in the leader-following multi-agent systems. Furthermore, there are several other
interesting topics that can be explored in future research. For instance, it would be valuable to investigate the
cooperatability of the leader-following multi-agent systems with both multiplicative noises and delays under
Markov switching topologies

DECLARATIONS
Authors’ contributions
Made substantial contributions to the research and investigation process, reviewed and summarized the liter-
ature, and wrote and edited the original draft: Li D
Performed oversight and leadership responsibility for the research activity planning and execution and per-
formed critical review, commentary, and revision: Li T

Availability of data and materials
Not applicable.

Financial support and sponsorship
Not applicable.

Conflicts of interest
All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.

Copyright
© The Author(s) 2023.

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