The effect of the interdependence between subnets on the spectral properties of Supra-Laplacian for partially interdependent networks is investigated. The theoretical approximate formulae of the minimum non-zero eigenvalue and the maximum eigenvalue of Supra-Laplacian for partially interdependent networks are derived, respectively. The outcomes are more general and need fewer calculations than that in other literature. The findings can be instructive for networks when linking to the spectral properties of the Supra-Laplacian. In addition, without changing the number and positions of the controllers, the influence of interdependence between directed subnets (controllable or uncontrollable) on the controllability of complex networks is discussed. Some sufficient conditions and necessary conditions for the controllability or uncontrollability of interdependent networks are presented. They will provide a new method for constructing a controllable actual interdependent network.