Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvalues

Shengbo Eben Li; Zhitao Wang; Yang Zheng; Diange Yang; Keyou You

doi:10.1016/j.eng.2020.05.006

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Engineering ›› 2020, Vol. 6 ›› Issue (6) : 688-694. DOI: 10.1016/j.eng.2020.05.006

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Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvalues

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Abstract

The time-varying network topology can significantly affect the stability of multi-agent systems. This paper examines the stability of leader–follower multi-agent systems with general linear dynamics and switching network topologies, which have applications in the platooning of connected vehicles. The switching interaction topology is modeled as a class of directed graphs in order to describe the information exchange between multi-agent systems, where the eigenvalues of every associated matrix are required to be positive real. The Hurwitz criterion and the Riccati inequality are used to design a distributed control law and estimate the convergence speed of the closed-loop system. A sufficient condition is provided for the stability of multi-agent systems under switching topologies. A common Lyapunov function is formulated to prove closed-loop stability for the directed network with switching topologies. The result is applied to a typical cyber–physical system—that is, a connected vehicle platoon—which illustrates the effectiveness of the proposed method.

Keywords

Stability / Multi-agent system / Switching topologies / Common Lyapunov function

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Shengbo Eben Li, Zhitao Wang, Yang Zheng, Diange Yang, Keyou You. Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvalues. Engineering, 2020, 6(6): 688‒694 https://doi.org/10.1016/j.eng.2020.05.006

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