 
Summary: Application of FiniteTime Stability Concepts to
the Control of ATM Networks
F. Amato # , M. Ariola + , C. T. Abdallah # , C. Cosentino §
March 21, 2003
Extended Abstract
1 Introduction
When dealing with the stability of a system, a distinction should be made
between classical Lyapunov Stability and FiniteTime Stability (FTS) (or Short
Time Stability). The concept of Lyapunov Asymptotic Stability is largely known
to the control community; on the other hand a system is said to be finitetime
stable if, once we fix a timeinterval, its state does not exceeds some bounds
during this timeinterval. Often asymptotic stability is enough for practical
applications, but there are some cases where large values of the state are not
acceptable, for instance in the presence of saturations. In these cases, we need
to check that these unacceptable values are not attained by the state; for these
purposes FTS could be used.
Some early results on FTS can be found in [9], [12] and [8]; more recently
the concept of FTS has been revisited in the light of recent results coming from
Linear Matrix Inequalities (LMIs) theory, which has allowed to find less conser
vative conditions guaranteeing FTS and finite time stabilization of uncertain,
