Exact computation of amplification for a class of nonlinear systems arising from cellular signaling pathways. Chaves, M. & Sontag, E. *Automatica*, 42:1987-1992, 2006. abstract bibtex A commonly employed measure of the signal amplification properties of an input/output system is its induced L2 norm, sometimes also known as H-infinity gain. In general, however, it is extremely difficult to compute the numerical value for this norm, or even to check that it is finite, unless the system being studied is linear. This paper describes a class of systems for which it is possible to reduce this computation to that of finding the norm of an associated linear system. In contrast to linearization approaches, a precise value, not an estimate, is obtained for the full nonlinear model. The class of systems that we study arose from the modeling of certain biological intracellular signaling cascades, but the results should be of wider applicability.

@ARTICLE{chaves_automatica06,
AUTHOR = {M. Chaves and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Exact computation of amplification for a class of
nonlinear systems arising from cellular signaling pathways},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1987-1992},
VOLUME = {42},
KEYWORDS = {systems biology, biochemical networks,
nonlinear stability, dynamical systems},
PDF = {../../FTPDIR/chaves_gains_comparison_automatica06.pdf},
ABSTRACT = { A commonly employed measure of the signal amplification
properties of an input/output system is its induced L2 norm,
sometimes also known as H-infinity gain. In general, however, it is
extremely difficult to compute the numerical value for this norm, or
even to check that it is finite, unless the system being studied is
linear. This paper describes a class of systems for which it is
possible to reduce this computation to that of finding the norm of an
associated linear system. In contrast to linearization approaches, a
precise value, not an estimate, is obtained for the full nonlinear
model. The class of systems that we study arose from the modeling of
certain biological intracellular signaling cascades, but the results
should be of wider applicability. }
}

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