Let (x) over dot = A(t)x + b(t)u be a time-variable linear system. We
cousider the problem for determination of the feedback control u = f(t
)x such that the closed system (x) over dot = (A(t) + b(t)f(t))x may b
e reducible using some group G of the lineal transformations. The nece
ssary conditions for G-reducibility are established.