Abstract
In this chapter, we aim to deal with the consensus analysis for general discrete-time linear multi-agent systems (MASs), which are allowed to be unstable. To this aim, we further develop the nonnegative matrix theory, which is widely used for analysis of multiple interacting integrators, to establish certain product properties of infinite row stochastic matrices. With the proposed approach, we finally show both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under mild conditions. More specifically, the individual uncoupled system is allowed to be strictly unstable (in the discrete-time sense), and it is only required that the joint of the communication topologies has a spanning tree frequently enough. Moreover, a lower bound of the convergence rate and an upper bound for the strictly unstable mode are specified. These bounds are proven to be independent of the switching mode of the communication topologies.
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Qin, J., Gao, H., Yu, C. (2022). On Discrete-Time Convergence for General Linear Multi-agent Systems Under Dynamic Topology. In: Tian, YC., Levy, D.C. (eds) Handbook of Real-Time Computing. Springer, Singapore. https://doi.org/10.1007/978-981-287-251-7_25
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DOI: https://doi.org/10.1007/978-981-287-251-7_25
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