Two-dimensional $\mathrm T$-systems of functions and their application for research of time optimal linear nonstationary control systems

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.