From the large system perspective, the directed complex dynamic network is considered as being composed of the nodes subsystem (NS) and the links subsystem (LS), which are coupled with together. Different from the previous studies which propose the dynamic model of LS with the matrix differential equations, this paper describes the dynamic behavior of LS with the outgoing links vector at every node, by which the dynamic model of LS can be represented as the vector differential equation to form the outgoing links subsystem (OLS). Since the vectors possess the flexible mathematical operational properties than matrices, this paper proposes the more convenient mathematic method to investigate the double tracking control problems of NS and OLS. Under the state of OLS can be unavailable, the asymptotical state observer of OLS is designed in this paper, by which the tracking controllers of NS and OLS are synthesized to ensure achieving the double tracking goals. Finally, the example simulations for supporting the theoretical results are also provided.