 
Summary: A note on stability of arbitrarily switched
homogeneous systems
David Angeli a
a Dip. Sistemi e Informatica,
Universita di Firenze,
Via di Santa Marta 3,
50139 Firenze, Italy
Abstract
A family of switched systems is exponentially stable if there exists positive constants
M and such that the solution at time t satises an estimate of the following
kind jx(t)j Me t jx(0)j, for all possible switching sequences. Clearly exponential
stability implies attractivity of the origin; we show that for homogeneous systems
(and as a special case for linear systems) the converse implication is also true.
Key words: stability properties, Lyapunov methods, switched systems, robust
stability
1 Introduction and basic denitions
The study of switched systems is a fastly growing area of research in control
theory. Informally a switched system is a dynamical system which is able to
commute between dierent behaviours according to some external input vari
able, which we will in the following refer to as switching signal. The practical
