Stabilization of Multi-agent Dynamical Systems for Cyclic Pursuit Behavior

This paper studies pursuit formation stability analysis and stabilization problems in target-enclosing operations by multiple dynamic agents. First, we introduce a D-stability problem by considering the requirements for multi- agent system's transient performance, and then develop a simple diagrammatic pursuit formation stability criterion. Then, as for the formation stabilization problem when agent's dynamics and its local controller are given, we develop an optimization problem subject to LMI constraints derived based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma to maximize the connectivity gain of a cyclic pursuit based on-line path generator. It provides a permissible range of gain, which guarantees the satisfaction not only of a global formation stability condition but also of a required performance specification. Finally, a constrained polynomial optimization problem is developed, in order to design agent's local controller parameters guaranteeing that a connectivity gain becomes the maximum one satisfying the global formation stability condition for a class of dynamic agents given a priori.