@article {2006,
title = {Common Polynomial Lyapunov Functions for Linear Switched Systems},
journal = {SIAM J. Control Optim. 45 (2006) 226-245},
number = {arXiv.org;math/0403209v2},
year = {2006},
abstract = {In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.},
doi = {10.1137/040613147},
url = {http://hdl.handle.net/1963/2181},
author = {Paolo Mason and Ugo Boscain and Yacine Chitour}
}