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A sampleddata composite system given by a set of vector difference equations is dealt wi t h. The system given by X~( T + 1) -XXT) = A i i f i [ x i ( r ) ] is referred to as the ith isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the A satisfy certain conditions and the leading principal minors of the determinant Ibijl, i, j = 1, . . . , n. are all positive. Here, the diagonal element bii is a positive number such that IIxi(r + 1)li -IXi(T)li 5 -hill fi[Xi(r)]I holds with regard to the motion of the ith isolated subsystem, and the nondiagonal element bij, i # j , is the minus of IIAijll, which is defined as the maximum of llAirrjll, for IIxjl = I. Some extensions of this result are also given. Composite relay controlled systems are studied as examples.