This article is concerned with formation stability analysis of 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 Lyapunov and asymptotic stability conditions which should hold for the above path generation laws. These conditions are derived based on a simple stability analysis method for linear systems with a generalised frequency variable. The formation control scheme combined with a cyclic pursuit based distributed on-line path generator satisfying the derived stability conditions guarantees the required global convergence property with theoretical rigour. Furthermore, in order to show its distinctive features clearly, we present how to analyse a global formation stability for multi-agent systems, where each agent is modelled as a class of second-order systems and is locally stabilised by a proportional-derivative (PD) controller. Some simulation examples illustrate the distinctive features of the proposed method and the achievement of a desired pursuit pattern.