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A bounded complementary sensitivity function ensures topology-independent stability of homogeneous dynamical networks

Blanchini, Franco; Casagrande, Daniele; Giordano, Giulia LU and Viaro, Umberto (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)
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author
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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
2018-01-07 12:15:37
@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},
  year         = {2017},
}