Geodesic
The structure of the attractor of shapes of reachable sets
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 74-81

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We study the asymptotic behavior of reachable sets of a linear time-invariant impulsive control system. Our main result is a complete description of the set of limit shapes of reachable sets (the attractor) in the case of a scalar control. The attractor is a torus defined via the pure imaginary eigenvalues of the system matrix.
Keywords: linear system, impulsive control, reachable (attainable) set, shape of convex body, attractor
Mots-clés : torus. 
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     author = {A. I. Ovseevich},
     title = {The structure of the attractor of shapes of reachable sets},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {74--81},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a6/}
}
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A. I. Ovseevich. The structure of the attractor of shapes of reachable sets. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 74-81. http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a6/