This paper studies a formation stability analysis scheme of a distributed cooperative control for target-enclosing operations by multiple homogeneous dynamic agents. To this end, we first present an on-line path generator design method based on a cyclic pursuit scheme. Then, we provide the stability condition which the developed path generator should satisfy. This condition is derived based on a simple stability analysis method for hierarchical large-scale linear systems with a generalized frequency variable. The formation control scheme combined with a cyclic pursuit based distributed on-line path generator satisfying the derived stability condition guarantees the required global convergence property with theoretical rigor. Further, in order to show its distinctive features clearly, we present how to analyze global formation stability for a class of multi-agent systems where each agent is modeled as a second-order system and is locally stabilized by the PID controller. A simulation example illustrates distinctive features of the proposed method and the achievement of a desired pursuit pattern.