Distributed Coordination D-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems

In this study, the cyclic pursuit formation stabilization problem in target-enclosing operations by multiple homogeneous dynamic agents is investigated. To this end, a Lyapunov D-stability problem is first formulated to cover the transient performance requirements for multi-agent systems. Then, a simple diagrammatic Lyapunov D-stability criterion for cyclic pursuit formation is derived. The formation control scheme combined with a cyclic-pursuit-based distributed online path generator satisfying this condition guarantees both the required transient performance and global convergence properties with theoretical rigor. It is shown that the maximization of the connectivity gain in a cyclic-pursuit-based online path generator can be reduced to an optimization problem subject to linear matrix inequality constraints derived using the generalized Kalman-Yakubovich–Popov lemma. This approach provides a permissible range of connectivity gain, which not only guarantees global formation stability/convergence properties but also satisfies the required performance specification. Several numerical examples are provided to confirm the effectiveness of the proposed method.