Geodesic
Invariant sets of control systems with distributed parameters with time delay
Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 70-78

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In this paper we consider the problem of finding conditions ensuring that a given set is strong or weak invariant with respect to control system with time delay. System is described by heat conductivity equation in right-hand side of which there is the control in additive form. Necessary and sufficient conditions were obtained for the invariance of a given set under a geometric restriction and sufficient conditions under an integral restriction. The given conditions differ from results for the control with time delay obtained earlier. 
@article{EMJ_2014_5_4_a4,
     author = {U. Ibragimov},
     title = {Invariant sets of control systems with distributed parameters with time delay},
     journal = {Eurasian mathematical journal},
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     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2014_5_4_a4/}
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U. Ibragimov. Invariant sets of control systems with distributed parameters with time delay. Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 70-78. http://geodesic.mathdoc.fr/item/EMJ_2014_5_4_a4/