  The paper continues the authors' study of the linearizability problem for
nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett.
134 (2019), 104572], conditions on mappability of a nonlinear control system to
a preassigned linear system with analytic matrices were obtained. In the
present paper we solve more general problem on linearizability conditions
without indicating a target linear system. To this end, we give a description
of invariants for linear non-autonomous single-input controllable systems with
analytic matrices, which allow classifying such systems up to transformations
of coordinates. This study leads to one problem from the theory of linear
ordinary differential equations with meromorphic coefficients. As a result, we
obtain a criterion for mappability of nonlinear control systems to linear
control systems with analytic matrices.
