Monotone control systems. Angeli, D. & Sontag, E. IEEE Trans. Automat. Control, 48(10):1684–1698, 2003. Errata are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/angeli-sontag-monotone-TAC03-typos.txt
abstract   bibtex   
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.
@ARTICLE{monotoneTAC,
   AUTHOR       = {D. Angeli and E.D. Sontag},
   JOURNAL      = {IEEE Trans. Automat. Control},
   TITLE        = {Monotone control systems},
   YEAR         = {2003},
   OPTMONTH     = {},
   NOTE         = {Errata are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/angeli-sontag-monotone-TAC03-typos.txt},
   NUMBER       = {10},
   PAGES        = {1684--1698},
   VOLUME       = {48},
   KEYWORDS     = {systems biology, biochemical networks, 
      nonlinear stability, dynamical systems, monotone systems},
   PDF          = {../../FTPDIR/angeli-sontag-monotone-TAC03.pdf},
   ABSTRACT     = { Monotone systems constitute one of the most important 
      classes of dynamical systems used in mathematical biology modeling. 
      The objective of this paper is to extend the notion of monotonicity 
      to systems with inputs and outputs, a necessary first step in trying 
      to understand interconnections, especially including feedback loops, 
      built up out of monotone components. Basic definitions and theorems 
      are provided, as well as an application to the study of a model of 
      one of the cell's most important subsystems. }
}

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