Based on state feedback and output feedback control methods, the bipartite state consensus tracking control problem for discrete linear leader-following multi-agent systems (MASs) is solved, where the leader has discrete autonomous dynamics and can generate ideal reference trajectory signal. Firstly, a new distributed state feedback control protocol is proposed based on the Gerschgorin circle theorem and the discrete algebraic Riccati equation. The control coupling gain based on the system topology matrix enables the global tracking error system locate in the stable region of the unit circle. Under the structurally balanced condition, it can be proved that the agents of two opposite subgroups under the signed directed graph can achieve bipartite state consensus using the Lyapunov stability theory and separation principle. Then, based on the cooperative-competitive interaction information of neighbours, a new distributed state observer is introduced to realize the tracking for the state of a follower. Furthermore, an observer-based output feedback bipartite control protocol is proposed to achieve the ideal leader-follower bipartite state tracking under the condition that the states are not known, which can also be applied to more general consensus control scenarios. Finally, two numerical examples are given to illurstrate the feasibility and effectiveness of the proposed algorithms.