Abstract
In this chapter, we further the study on consensus for multiple generic linear systems by considering directed switching network topology.
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Notes
- 1.
The condition on the communication graph is changed to be the jointly connected communication graph in undirected context, see, e.g., [2, 27, 76].
- 2.
The details of how to calculate \(\alpha \) are referred to [88] and omitted here for brevity.
- 3.
The boundedness of \(g(\cdot )\) within bounded time intervals means that given any time interval of length \(l>0\), there exists a constant b(l) depending only on l such that \(g(\psi ^i_{\sigma (t)})<b(l)\) with \(\mathbf {y}_i^{UB}\) being replaced by \(\mathbf {y}_i\).
- 4.
A matrix is said to be marginally stable if all its eigenvalues have non-positive real part and those with zero real part are semi-simple.
- 5.
If in a graph, whenever \(w_{ij}\ne 0\), there holds that \(w_{ji}\ne 0\), then the graph is said to be bidirected. It is obvious that an undirected graph is bidirected.
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Qin, J., Ma, Q., Gao, H., Zheng, W.X., Kang, Y. (2022). Generic Linear Systems over Directed Switching Network Topology. In: Consensus Over Switching Network Topology: Characterizing System Parameters and Joint Connectivity. Studies in Systems, Decision and Control, vol 393. Springer, Cham. https://doi.org/10.1007/978-3-030-85657-1_4
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DOI: https://doi.org/10.1007/978-3-030-85657-1_4
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