In this paper, we consider a leader-follower problem for a group of homogeneous linear time invariant (LTI) follower agents that are interacting over a directed acyclic graph. In our problem of interest, only a subset of the follower agents has access to the state of the leader in specific sampling times. The dynamics of the leader that generates its states is unknown to the followers. For interaction topologies in which the leader is a global sink in the graph, we propose a distributed algorithm that allows the agents to arrive at the sampled state of the leader before the next sample arrives. We prove that the control input to take the followers from one sampled state to the next one is minimum energy for all the followers. We also show that after the first sampling epoch, the states of all the follower agents are synchronized with each other. We demonstrate the application of our proposed algorithm for two leader-follower problems for mobile agents. Our first example shows the application of our algorithm in control of unicycle robots in a formation motion. In the second example, we demonstrate the use of our algorithm for reference state tracking via a group of second order integrator followers with bounded control. In this example, we show that the properties of our proposed leader-follower algorithm allow us to design the arrival times at the reference states in such a way that the input bounds of the agents never get violated.