This paper studies a design methodology of a distributed cooperative controller for target-enclosing operations by multiple 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 large-scale linear systems with 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. Simulation examples illustrate its distinctive features and the achievement of a desired pursuit pattern.