Stability margin of undirected homogeneous relative sensing networks: A geometric perspective
- Hamdipoor, Vahid; Moon, Jun; Kim, Yoonsoo
- Issue Date
- Stability margin; Relative sensing network; Laplacian matrix; Nyquist plot; Curvature
- SYSTEMS & CONTROL LETTERS, v.156
- Journal Title
- SYSTEMS & CONTROL LETTERS
- In this paper, we study the stability margin (SM) of undirected homogeneous relative sensing networks (UH-RSNs) from a geometric point of view. SM is an important robustness measure indicating the amount of simultaneous gain and phase perturbations in the feedback channels before the instability occurs. A UH-RSN is characterized by the identical local dynamics (a single-input-single-output (SISO) open-loop transfer function T-loc(s)) of individual agent and the graph Laplacian L-g representing how the agents are connected. It is shown in this paper that UH-RSNs having multiple inputs and outputs in general may be represented as a unity feedback system including the SISO T-loc(s) and one of the real eigenvalues of L-g. This representation then helps to identify a class of cooperative T-loc(s) for which (1) SM becomes maximized or equal to 1 when the network's connectivity (the second smallest eigenvalue of L-g is greater than or equal to the curvature of the Nyquist plot of T-loc(s) at the origin; and (2) two bounds on SM are obtained for the SM estimation based on the geometric shape of Nyquist plot. Also, the representation of unity feedback system implies that UH-RSNs with non-cooperative T-loc(s) become unstable when the agents are joined with high connectivity. Numerical examples are provided to demonstrate these findings. (C) 2021 Elsevier B.V. All rights reserved.
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- 공학계열 > Division of Mechanical and Aerospace Engineering > Journal Articles
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