A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections. Sontag, E. and Ingalls, B. J. Franklin Inst., 339(2):211–229, 2002.
abstract   bibtex   
A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.
@ARTICLE{sontag_ingalls_small_gain_JFI02,
   AUTHOR       = {E.D. Sontag and B.P. Ingalls},
   JOURNAL      = {J. Franklin Inst.},
   TITLE        = {A small-gain theorem with applications to input/output 
      systems, incremental stability, detectability, and interconnections},
   YEAR         = {2002},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {2},
   PAGES        = {211--229},
   VOLUME       = {339},
   KEYWORDS     = {input to state stability},
   PDF          = {../../FTPDIR/small-gain-as-published.pdf},
   ABSTRACT     = { A general ISS-type small-gain result is presented. It 
      specializes to a small-gain theorem for ISS operators, and it also 
      recovers the classical statement for ISS systems in state-space form. 
      In addition, we highlight applications to incrementally stable 
      systems, detectable systems, and to interconnections of stable 
      systems. }
}
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