Forward completeness, unboundedness observability, and their Lyapunov characterizations. Angeli, D. & Sontag, E. Systems Control Lett., 38(4-5):209–217, 1999. abstract bibtex 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.
@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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