Kalman's controllability rank condition: from linear to nonlinear. Sontag, E. In Mathematical system theory, pages 453–462. Springer, Berlin, 1991.
abstract   bibtex   
The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article presents an elementary and expository overview of the generalizations of this test to a condition for testing accessibility of discrete and continuous time nonlinear systems.
@INCOLLECTION{MR1296059,
   AUTHOR       = {E.D. Sontag},
   BOOKTITLE    = {Mathematical system theory},
   PUBLISHER    = {Springer},
   TITLE        = {Kalman's controllability rank condition: from linear to 
      nonlinear},
   YEAR         = {1991},
   ADDRESS      = {Berlin},
   OPTCHAPTER   = {},
   OPTCROSSREF  = {},
   OPTEDITION   = {},
   OPTEDITOR    = {},
   OPTMONTH     = {},
   OPTNOTE      = {},
   OPTNUMBER    = {},
   PAGES        = {453--462},
   OPTSERIES    = {},
   OPTTYPE      = {},
   OPTVOLUME    = {},
   KEYWORDS     = {controllability},
   PDF          = {../../FTPDIR/rek-volume.pdf},
   ABSTRACT     = { The notion of controllability was identified by Kalman 
      as one of the central properties determining system behavior. His 
      simple rank condition is ubiquitous in linear systems analysis. This 
      article presents an elementary and expository overview of the 
      generalizations of this test to a condition for testing accessibility 
      of discrete and continuous time nonlinear systems. }
}

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