@ARTICLE{MR1754903,
   AUTHOR       = {D. Angeli and E.D. Sontag},
   JOURNAL      = {Systems Control Lett.},
   TITLE        = {Forward completeness, unboundedness observability, and 
      their Lyapunov characterizations},
   YEAR         = {1999},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {4-5},
   PAGES        = {209--217},
   VOLUME       = {38},
   KEYWORDS     = {observability, input to state stability, 
      dynamical systems},
   PDF          = {../../FTPDIR/uo.pdf},
   ABSTRACT     = { A finite-dimensional continuous-time system is forward 
      complete if solutions exist globally, for positive time. This paper 
      shows that forward completeness can be characterized in a necessary 
      and sufficient manner by means of smooth scalar growth inequalities. 
      Moreover, a version of this fact is also proved for systems with 
      inputs, and a generalization is also provided for systems with 
      outputs and a notion (unboundedness observability) of relative 
      completeness. We apply these results to obtain a bound on reachable 
      states in terms of energy-like estimates of inputs. }
}

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