Seminar Details
2011-10-25 (14.00) : Stability of Linear Switched Systems
At Euler building
Organized by Mathematical Engineering
Speaker :
Moussa BALDE (UCAD Dakar)
Abstract :
The talk is about asymptotic stability properties of linear switched
systems.
For the planar linear switched system d/dt x(t) = u(t) A_1
x(t)+(1-u(t)) A_2 x(t), where the real matrices A_1, A_2 in R^{2×2} are
Hurwitz and u(·) : [0, infty[ --> {0, 1} is a measurable function, we
give a coordinate-invariant necessary and sufficient condition on
A_1 and A_2 under which the system is asymptotically stable for
arbitrary switching functions u(.). This condition is mainly given
in terms of the polar form of the determinant map Gamma(A_1,A_2) = 1/2
(tr(A_1)tr(A_2) - tr(A_1 A_2)).
Then under the hypothesis that p subsystems in R^d share a non strict
quadratic Lyapunov function, we provide a large class of switching
signals for which a large class of switched systems are asymptotically
stable. For this purpose we define what we call non chaotic inputs,
which generalize the different notions of inputs with dwell time.
Keywords: Switched systems; Asymptotic stability; Quadratic Lyapunov
functions; Chaotic signals; Omega-limit sets.