The author considers the stabilization problem for the system \(\dot x_ 1=A_{11}x_ 1+A_{12}x_ 2+B_ 1u\), \(x_ 1\in {\mathbb{R}}^{n_ 1}\), \(\epsilon\) \(\dot x_ 2=A_{21}x_ 1+A_{22}x_ 2+B_ 2u\), \(x_ 2\in {\mathbb{R}}^{n_ 2}\), \(y=C_ 1x_ 1+C_ 2x_ 2\), \(y\in {\mathbb{R}}^ p\), \(u\in {\mathbb{R}}^ m\), \(0<\epsilon \ll 1\), where \(A_{22}\) is assumed invertible. Under some conditions it is proved that stabilizing control for sufficiently small \(\epsilon\) takes the form \(u=Gy\), \(G=G^ 0_ 1(I+D_ 0G^ 0_ 1)+G^ 0_ 2\) where \(D_ 0=-C_ 2A^{- 1}_{22}B_ 2\), \(G^ 0_ 1\) being the stabilizing feedback gain for the reduced system and \(G^ 0_ 2\) the stabilizing feedback gain for the fast subsystem.