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On the minimal degree of common Lyapunov polynomial functions for planar switched systems

Speaker: 
P. Mason
Institution: 
SISSA
Schedule: 
Wednesday, March 26, 2003 - 06:30 to 07:30
Location: 
room L
Abstract: 

We consider planar switched systems of the type x'= u(t)Ax(t)+(1-u(t))Bx(t) , where x is in R^2 and A,B are 2x2 matrices, which are asymptotically stable at the origin for every switching function u:[0,+inf)->[0,1] . It is well-known that there are systems of this form such that a common quadratic Lyapunov function does not exist. Anyway the problem of finding an upper bound on the minimal degree of a common Lyapunov polynomial function was open up to now. We answer to this question proving that such a bound actually does not exist.

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