A bounded complementary sensitivity function ensures topology-independent stability of homogeneous dynamical networks
(2017) In IEEE Transactions on Automatic Control- Abstract
- This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the infinity-norm of the complementary sensitivity function NF(s)G(s)/[1+NF(s)G(s)] is less than 1. This bound is non-conservative. When nodes and arcs transferences are affected by... (More)
- This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the infinity-norm of the complementary sensitivity function NF(s)G(s)/[1+NF(s)G(s)] is less than 1. This bound is non-conservative. When nodes and arcs transferences are affected by uncertainties with norm bound K>0, topology-independent stability is robustly ensured if the infinity-norm is less than 1/(1+2NK). For symmetric systems, stability is guaranteed for all topologies with interaction degree at most N if the Nyquist plot of NF(s)G(s) does not intersect the real axis to the left of -1/2. The proposed results are applied to fluid networks and platoon formation. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/85d65789-e75a-4e56-a97e-820b18ba210a
- author
- Blanchini, Franco ; Casagrande, Daniele ; Giordano, Giulia LU and Viaro, Umberto
- organization
- publishing date
- 2017
- type
- Contribution to journal
- publication status
- published
- subject
- in
- IEEE Transactions on Automatic Control
- issue
- 99
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85029002008
- ISSN
- 1558-2523
- DOI
- 10.1109/TAC.2017.2737818
- language
- English
- LU publication?
- yes
- id
- 85d65789-e75a-4e56-a97e-820b18ba210a
- date added to LUP
- 2017-08-22 11:33:14
- date last changed
- 2024-05-12 19:12:59
@article{85d65789-e75a-4e56-a97e-820b18ba210a,
abstract = {{This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the infinity-norm of the complementary sensitivity function NF(s)G(s)/[1+NF(s)G(s)] is less than 1. This bound is non-conservative. When nodes and arcs transferences are affected by uncertainties with norm bound K>0, topology-independent stability is robustly ensured if the infinity-norm is less than 1/(1+2NK). For symmetric systems, stability is guaranteed for all topologies with interaction degree at most N if the Nyquist plot of NF(s)G(s) does not intersect the real axis to the left of -1/2. The proposed results are applied to fluid networks and platoon formation.}},
author = {{Blanchini, Franco and Casagrande, Daniele and Giordano, Giulia and Viaro, Umberto}},
issn = {{1558-2523}},
language = {{eng}},
number = {{99}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Automatic Control}},
title = {{A bounded complementary sensitivity function ensures topology-independent stability of homogeneous dynamical networks}},
url = {{http://dx.doi.org/10.1109/TAC.2017.2737818}},
doi = {{10.1109/TAC.2017.2737818}},
year = {{2017}},
}