Summary: Forward Completeness, Unboundedness
Observability,
and their Lyapunov Characterizations
David Angeli a Eduardo D. Sontag b
a Dip. Sistemi e Informatica,
Universit`a di Firenze,
Via di Santa Marta 3,
50139 Firenze, Italy
b Dep. of Mathematics,
Rutgers University,
New Brunswick, NJ 08903
Abstract
A finite­dimensional continuous­time system is forward complete if solutions exist
globally, for positive time. This paper shows that forward completeness can be char­
acterized 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 in­
puts, 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 energy­like estimates of inputs.
Key words: stability properties, Lyapunov methods, global existence of solutions,

Source: Angeli, David - Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze

Collections: Engineering