Aggregates of positive impulse response systems: A decomposition approach for complex networks

Franco Bianchini, Christian Cuba Samaniego, Elisa Franco, Giulia Giordano

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
8 Downloads (Pure)


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.

Original languageEnglish
Title of host publicationProceedings of the 2017 IEEE 56th Annual Conference on Decision and Control
EditorsA Astolfi et al
Place of PublicationPiscataway, NJ, USA
ISBN (Electronic)978-150902873-3
Publication statusPublished - 2017
EventCDC 2017: 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017


ConferenceCDC 2017: 56th IEEE Annual Conference on Decision and Control
OtherThe CDC is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control. The CDC annually brings together an international community of researchers and practitioners in the field of automatic control to discuss new research results, perspectives on future developments, and innovative applications relevant to decision making, systems and control, and related areas.
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