A sampled-data composite system given by a set of vector difference equations x_{i}(\tau + 1) - x_{i}(\tau) = \sum \min{j = 1} \max{n} A_{ij} f_{j}[x_{j}(\tau)], i = 1 ..., n is dealt with. The system given by x_{i}(\tau + 1) - x_{i}(\tau) = A_{ij} f_{i}[x_{i}(\tau)] is referred to as the i th isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the f i satisfy certain conditions and the leading principal minors of the determinant |b_{ij}|, i,j = 1, ..., n, are all positive. Here, the diagonal element b ii is a positive number such that \|x_{i}(\tau + 1)\| - \|x_{i}(\tau) \| \leq - b_{ij}\| f_{i}[x_{i}(\tau)]\| holds with regard to the motion of the i th isolated subsystem, and the nondiagonal element b_{ij} , i \neq j , is the minus of \|A_{ij}\| , which is defined as the maximum of \|A_{ij}x_{j}\| , for \|x_{j}\| = 1 . Some extensions of this result are also given. Composite relay controlled systems are studied as examples.
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