Geodesic
Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1855-1864

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A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs. 
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     author = {N. B. Brusnikina and A. V. Lotov},
     title = {Guaranteed-accuracy approximation of reachable sets for a~linear dynamic system subject to impulse actions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1855--1864},
     publisher = {mathdoc},
     volume = {47},
     number = {11},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a4/}
}
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N. B. Brusnikina; A. V. Lotov. Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1855-1864. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a4/