@INPROCEEDINGS{iglesias_ifac08,
   AUTHOR       = {B. Andrews and E.D. Sontag and P. Iglesias},
   BOOKTITLE    = {Proc. 17th IFAC World Congress, Seoul},
   TITLE        = {An approximate internal model principle: Applications to 
      nonlinear models of biological systems},
   YEAR         = {2008},
   OPTADDRESS   = {},
   OPTCROSSREF  = {},
   OPTEDITOR    = {},
   OPTMONTH     = {},
   OPTNOTE      = {},
   OPTNUMBER    = {},
   OPTORGANIZATION = {},
   PAGES        = {Paper FrB25.3, 6 pages},
   OPTPUBLISHER = {},
   OPTSERIES    = {},
   OPTVOLUME    = {},
   KEYWORDS     = {biological adaptation, internal model principle},
   PDF          = {../../FTPDIR/andrews_sontag_iglesias_approximate_internal_model_IFAC2008.pdf},
   ABSTRACT     = {The proper function of many biological systems requires 
      that external perturbations be detected, allowing the system to adapt 
      to these environmental changes. It is now well established that this 
      dual detection and adaptation requires that the system have an 
      internal model in the feedback loop. In this paper we relax the 
      requirement that the response of the system adapt perfectly, but 
      instead allow regulation to within a neighborhood of zero. We show, 
      in a nonlinear setting, that systems with the ability to detect input 
      signals and approximately adapt require an approximate model of the 
      input. We illustrate our results by analyzing a well-studied 
      biological system. These results generalize previous work which 
      treats the perfectly adapting case. }
}

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