Geodesic
Two-dimensional $\mathrm T$-systems of functions and their application for research of time optimal linear nonstationary control systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2009), pp. 101-130

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The notion of $\rm TA$-system is introduced for a two-dimensional family of functions. This concept generalizes the well-known notion of $\rm T$-system for a one-dimensional family of functions. A number of statements about $\rm TA$-systems of functions is formulated and proved. The developed theory of $\rm TA$-systems is used to studying of linear non-stationary control systems. For such systems the time optimal problem is solved provided the initial point belongs the interior of the subcritical set.
Keywords: Tchebyshev systems of functions, $\mathrm T$-systems, linear nonstationary control systems, time optimal control problem, time optimal function, subcritical systems, positional control. 
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     author = {V. V. Lukyanov},
     title = {Two-dimensional $\mathrm T$-systems of functions and their application for research of time optimal linear nonstationary control systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {101--130},
     publisher = {mathdoc},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_1_a4/}
}
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V. V. Lukyanov. Two-dimensional $\mathrm T$-systems of functions and their application for research of time optimal linear nonstationary control systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2009), pp. 101-130. http://geodesic.mathdoc.fr/item/VUU_2009_1_a4/