%0 Journal Article
%J SIAM J. Control Optim. 45 (2006) 226-245
%D 2006
%T Common Polynomial Lyapunov Functions for Linear Switched Systems
%A Paolo Mason
%A Ugo Boscain
%A Yacine Chitour
%X 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.
%B SIAM J. Control Optim. 45 (2006) 226-245
%G en_US
%U http://hdl.handle.net/1963/2181
%1 2063
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T14:36:21Z\\nNo. of bitstreams: 1\\n0403209v2.pdf: 244831 bytes, checksum: 1762d79876f9eb915a68dbc25d9a3a21 (MD5)
%R 10.1137/040613147