What is it about?
In order to stabilize a networked system for a cyclic graph, it is essential that control action is also located within the cycle. Moreover, we show that also the type of control action that is available in the system makes a difference: While in general pure Neumann control action is not sufficient for stabilization, with additional Dirichlet control action within the cycle the system can be stabilized.
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Why is it important?
In many applications that concern networked systems, the graphs that correspond to the networks regularly contain several cycles. Therefore in order to develop a stability theory for such applications, it is essential that the case of cyclic networks is also studied.
Perspectives
While in this contribution we have considered a network with a single cycle, we expect that results of a similar type also hold for networks that contain intertwined cycles.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: Stabilization of a cyclic network of strings by nodal control, Journal of Evolution Equations, December 2024, Springer Science + Business Media,
DOI: 10.1007/s00028-024-01030-0.
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