Aggregates of positive impulse response systems

A decomposition approach for complex networks

Conference paper (2017)

Authors

Franco Blanchini Università degli Studi di Udine
Christian Cuba Samaniego University of California
Elisa Franco University of California
G. Giordano Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering
Research Group
Team Tamas Keviczky (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2017 Franco Bianchini, Christian Cuba Samaniego, Elisa Franco, G. Giordano
DOI
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https://doi.org/10.1109/CDC.2017.8263939
More Info
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Published Date

2017

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Tamas Keviczky

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.

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