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A Lyapunov approach to incremental stability properties David Angeli

Summary: A Lyapunov approach to incremental stability properties
David Angeli 
Dip. di Sistemi e Informatica
Universita di Firenze
Via di S. Marta 3, 50139 Firenze, Italy
Email: angeli@dsi.unifi.it
Abstract. This paper deals with several notions of incremental stability. In other words, the
focus is on stability of trajectories with respect to one another, rather than with respect to some
attractor. The aim is to present a framework for understanding such questions fully compatible with
the well-known Input-to-State Stability approach. Applications of the newly introduced stability
notions are also discussed.
1 Introduction
Input-to-State stability (iss for short) has proven a valid instrument in order to study questions of
robust stability for nite-dimensional nonlinear systems. One reason for that is the possibility of
dealing, at the same time, with a body of theory which nicely extends to non-autonomous systems
the classic Lyapunov while still allowing for input-output descriptions of the system behavior, [11,
21, 27, 29]. In this way tools such as small-gain theorems [12] and Lyapunov dissipation inequalities
[26] have come together in a uni ed framework which bridges the gap between the state-space and
input-output approaches.
Stability properties are described through the use of comparison functions, the so called class K


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


Collections: Engineering