00956nas a2200133   4500008004100000245008400041210006900125260000900194520052900203100001700732700001700749700002000766856003600786       2004                        en  d00aOn the minimal degree of a common Lyapunov function for planar switched systems0 aminimal degree of a common Lyapunov function for planar switched  bIEEE3 aIn this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine  uhttp://hdl.handle.net/1963/4834