Geodesic
Discrete control systems with delay in~$\mathbb{R}^n$
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 123-138

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It's proved that the viability set coincide with sojourn set for discrete dynamic systems with delay. The sufficient conditions of the aim set is the viability set have been obtained. 
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     author = {O. S. Nechaeva},
     title = {Discrete control systems with delay in~$\mathbb{R}^n$},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {123--138},
     publisher = {mathdoc},
     number = {1},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2005_1_a8/}
}
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O. S. Nechaeva. Discrete control systems with delay in~$\mathbb{R}^n$. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 123-138. http://geodesic.mathdoc.fr/item/VUU_2005_1_a8/