Monotone systems under positive feedback: multistability and a reduction theorem. Enciso, G. & Sontag, E. Systems Control Lett., 54(2):159–168, 2005.
abstract   bibtex   
For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a previous paper provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties. New results characterizing strong monotonicity of feedback loops involving cascades are also presented.
@ARTICLE{enciso_sontagSCL05,
   AUTHOR       = {G.A. Enciso and E.D. Sontag},
   JOURNAL      = {Systems Control Lett.},
   TITLE        = {Monotone systems under positive feedback: multistability 
      and a reduction theorem},
   YEAR         = {2005},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {2},
   PAGES        = {159--168},
   VOLUME       = {54},
   KEYWORDS     = {multistability, systems biology, biochemical networks, 
      nonlinear stability, dynamical systems, monotone systems},
   PDF          = {../../FTPDIR/enciso_sontag_multistability_SCL04_inpress.pdf},
   ABSTRACT     = { For feedback loops involving single input, single 
      output monotone systems with well-defined I/O characteristics, a 
      previous paper provided an approach to determining the location and 
      stability of steady states. A result on global convergence for 
      multistable systems followed as a consequence of the technique. The 
      present paper extends the approach to multiple inputs and outputs. A 
      key idea is the introduction of a reduced system which preserves 
      local stability properties. New results characterizing strong 
      monotonicity of feedback loops involving cascades are also presented. }
}
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