Abstract: This paper is a note on the necessary and sufficient conditions of stability[1], observability and controllability[2] for interval matrices. An explicit definition of the union operator "U" is given, and an interval matrix can be expressed concretely as the union of its sub-interval matrices. It is illustrated that the property of stability, observability and controllability of an interval matrix (i. e. , a family of infinite number of matrices) is equivalent to the corresponding property of certain finite number of matrices. Also, an approach to seek the sub-interval matrices is proposed.