Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated experimentally, a rigorous theoretical certification of their stability is currently missing. This work fills this gap by providing the first formal stability analysis for a generic class of floating rigid bodies subject to spurious forces. We introduce a canonical model and construct a Lyapunov-based proof establishing local exponential stability of the hovering equilibrium. Crucially, the analysis explicitly addresses the structural challenges - specifically the induced non-minimum-phase behavior - that prevent the application of standard cascade arguments.

翻译：标准几何控制依赖于力-矩解耦假设，该假设在许多飞行平台中因控制力矩自然诱导的寄生力而失效。尽管针对此类耦合系统的控制策略已通过实验验证，但目前缺乏对其稳定性的严格理论证明。本研究填补了这一空白，首次对受寄生力作用的一类通用浮游刚体进行了形式化稳定性分析。我们提出了一个规范模型，并构建了基于李雅普诺夫理论的证明，确立了悬停平衡点的局部指数稳定性。关键之处在于，该分析明确解决了结构上的挑战——特别是诱导的非最小相位行为——这些挑战阻碍了标准级联论证方法的应用。