Abstract:
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.