Daniel Myklatun Tveit
Department of Electrical Engineering and Computer Science, University of Stavanger, Norway
Kristian Thorsen
Department of Electrical Engineering and Computer Science, University of Stavanger, Norway
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http://dx.doi.org/10.3384/ecp17138108Published in: Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th – 27th, 2017
Linköping Electronic Conference Proceedings 138:14, p. 108-113
Published: 2017-09-27
ISBN: 978-91-7685-417-4
ISSN: 1650-3686 (print), 1650-3740 (online)
Homeostasis refers to the ability of organisms and cells to
maintain a stable internal environment even in the presence
of a changing external environment. On the cellular
level many compounds such as ions, pH, proteins,
and transcription factors have been shown to be tightly
regulated, and mathematical models of biochemical networks
play a major role in elucidating the mechanisms
behind this behaviour. Of particular interest is the control
theoretic properties of these models, e.g. stability and
robustness. The simplest models consist of two components,
a controlled compound and a controller compound.
We have previously explored how signalling between
these two compounds can be arranged in order for
the network to display homeostasis, and have constructed
a class of eight two-component reaction kinetic networks
with negative feedback that shows set-point tracking and
disturbance rejection properties. Here, we take a closer
look at the stability and robust control inherent to this
class of systems. We show how these systems can be
described as negative feedback connections of two nonlinear
sub-systems, and show that both sub-systems are
output strictly passive and zero-state detectable. Using a
passivity-based approach, we show that all eight systems
in this class of two-component networks are asymptotically
stable.
Passivity, homeostasis, adaptation, stability,
robust control, integral control, negative feedback