TY - JOUR
T1 - Common Polynomial Lyapunov Functions for Linear Switched Systems
JF - SIAM J. Control Optim. 45 (2006) 226-245
Y1 - 2006
A1 - Paolo Mason
A1 - Ugo Boscain
A1 - Yacine Chitour
AB - 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.
UR - http://hdl.handle.net/1963/2181
U1 - 2063
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -