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An almost global notion of Input-to-State Stability David Angeli

Summary: An almost global notion of Input-to-State Stability
David Angeli
Dip. di Sistemi e Informatica
Universita di Firenze
Via di S. Marta, 3
50139 FIRENZE, Italy
Abstract. A new de nition of almost global Input-to-State Stability for systems on di er-
entiable manifolds is discussed. Some of its properties are investigated and speci c examples
are shown which can be treated by means of dual Lyapunov techniques.
1 Introduction and motivations
One of the central topics in control theory has been, since its very beginning, the study of
stability. For nite dimensional linear systems, most of the existing stability notions collapse
into few basic concepts that are precisely characterized in algebraic terms. Nonlinear systems,
on the other hand, exhibit a much broader variety of behaviours to be labeled either as stable
or unstable. The universe of possible stability notions is therefore much more diversi ed.
A fundamental chapter in the study of such notions is the quest for checkable conditions
which may serve in order to estabilish stability of a system without knowing explicitly its
solutions. A key contribution in this respect dates back to the works of Lyapunov, [7]. Its
second method for stability analysis allows to prove local and global stability properties on


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


Collections: Engineering