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Aggregates of Positive Impulse Response systems: a decomposition approach for complex networks

Blanchini, Franco ; Cuba Samaniego, Christian ; Franco, Elisa and Giordano, Giulia LU (2018) 56th IEEE Annual Conference on Decision and Control, CDC 2017
Abstract
To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally... (More)
To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally ensured (for any choice of the PIR subsystems) if a Metzler matrix depending on the interaction weights is Hurwitz; this condition is non-conservative. We also show how to compute an influence matrix that represents the steady-state effects of the interactions among PIR subsystems. (Less)
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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of the 56th IEEE Conference on Decision and Control
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
56th IEEE Annual Conference on Decision and Control, CDC 2017
conference location
Melbourne, Australia
conference dates
2017-12-12 - 2017-12-15
external identifiers
  • scopus:85046145021
DOI
10.1109/CDC.2017.8263939
language
English
LU publication?
yes
id
07685313-0d96-45e8-8211-c3e87d4f9311
date added to LUP
2017-08-22 11:40:59
date last changed
2022-04-01 18:52:20
@inproceedings{07685313-0d96-45e8-8211-c3e87d4f9311,
  abstract     = {{To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally ensured (for any choice of the PIR subsystems) if a Metzler matrix depending on the interaction weights is Hurwitz; this condition is non-conservative. We also show how to compute an influence matrix that represents the steady-state effects of the interactions among PIR subsystems.}},
  author       = {{Blanchini, Franco and Cuba Samaniego, Christian and Franco, Elisa and Giordano, Giulia}},
  booktitle    = {{Proceedings of the 56th IEEE Conference on Decision and Control}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Aggregates of Positive Impulse Response systems: a decomposition approach for complex networks}},
  url          = {{http://dx.doi.org/10.1109/CDC.2017.8263939}},
  doi          = {{10.1109/CDC.2017.8263939}},
  year         = {{2018}},
}