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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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