Forward completeness, unboundedness observability, and their Lyapunov characterizations

A finite-dimensional continuous-time system is forward complete if solution s exist globally, for positive time. This paper shows that forward complete ness 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. (C) 1999 Elsevier Science B.V . All rights reserved.