TY - Generic
T1 - On the minimal degree of a common Lyapunov function for planar switched systems
T2 - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3
Y1 - 2004
A1 - Paolo Mason
A1 - Ugo Boscain
A1 - Yacine Chitour
AB - In 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.
JF - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3
PB - IEEE
UR - http://hdl.handle.net/1963/4834
U1 - 4611
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -