This paper explores the stability of a class of multi-agent systems with proposed relay tracking strategy over a finite time interval. In this paper, agents are deployed in an area to monitor and track the intruded targets. According to proposed relay tracking strategy, the tracking agents and their communication topologies switch during the whole tracking process. This results in impulsive effects on the overall tracking errors. The relationship of finite time interval against desired overall tracking errors and control parameter is derived quantitatively for the multi-agent relay tracking system. Moreover, stability conditions for the system with disturbances and impulsive effects are obtained. Performance of proposed relay tracking strategy and correctness of derived results on stability over finite time intervals are demonstrated by a set of simulations.