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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