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Summary: Intrinsic robustness of global asymptotic
stability
David Angeli a
a Dip. Sistemi e Informatica,
Universita di Firenze,
Via di Santa Marta 3,
50139 Firenze, Italy
Abstract
Equivalence is shown for discrete time systems between global asymptotic stability
and the so called integral Input to State Stability. The latter is a notion of robust
stability with respect to exogenous disturbances which informally translates into
the statement \no matter what is the initial condition, if the energy of the inputs
is small, then the state must eventually be small".
Key words: Stability properties, Lyapunov methods, Robust stability, Nonlinear
systems
1 Introduction
The problem of external stability for non-linear systems has been addressed
in many di erent ways. A traditional approach, basically inspired by linear
systems theory, is the l p Bounded Input Bounded Output paradigm. In this
context stability means satisfaction of an inequality between norms of input
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