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Séminaire des thésards du 14 novembre 2014

Geometric and asymptotic properties of linear switched systems

Consider the linear switched system of the form \dotx(t)=A(t) x(t), where x belongs to R^n and A(\cdot) is any measurable function taking values on a compact and convex subset of the set of n*n real matrices with zero maximal Lyapunov exponent. When the system is irreducible then a Barabanov norm exists. In this talk, we will first focus on the geometric properties of Barabanov norms such as their regularity, their uniqueness up to homogeneity and their strict convexity. We will next study the asymptotic properties of the extremal trajectories associated with that system for n=3. Finally, the last part will be devoted to the study of a special system, namely the one based on a pair of 3*3 real Hurwitz matrices with rank-one difference.

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