Geodesic
On the boundedness of outer polyhedral estimates for reachable sets of linear systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 974-989

Voir la notice de l'article provenant de la source Math-Net.Ru

New properties of outer polyhedral (parallelepipedal) estimates for reachable sets of linear differential systems are studied. For systems with a stable matrix, it is determined what the orientation matrices are for which the estimates possessing the generalized semigroup property are bounded/unbounded on an infinite time interval. In particular, criteria are found (formulated in terms of the eigenvalues of the system's matrix and the properties of bounding sets) that guarantee for previously mentioned tangent estimates and estimates with a constant orientation matrix that either there are initial orientation matrices for which the corresponding estimate tubes are bounded or all these tubes are unbounded. For linear stationary systems, a system of ordinary differential equations and algebraic relations is derived that determines estimates with constant orientation matrices for reachable sets that have no generalized semigroup property but are tangent and also bounded if the matrix of the system is stable. 
@article{ZVMMF_2008_48_6_a3,
     author = {E. K. Kostousova},
     title = {On the boundedness of outer polyhedral estimates for reachable sets of linear systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {974--989},
     publisher = {mathdoc},
     volume = {48},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a3/}
}
TY  - JOUR
AU  - E. K. Kostousova
TI  - On the boundedness of outer polyhedral estimates for reachable sets of linear systems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 974
EP  - 989
VL  - 48
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a3/
LA  - ru
ID  - ZVMMF_2008_48_6_a3
ER  - 
%0 Journal Article
%A E. K. Kostousova
%T On the boundedness of outer polyhedral estimates for reachable sets of linear systems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 974-989
%V 48
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a3/
%G ru
%F ZVMMF_2008_48_6_a3
E. K. Kostousova. On the boundedness of outer polyhedral estimates for reachable sets of linear systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 974-989. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a3/