For a canonical form of mechanical systems defined through gradients of potential energy and dissipative terms, the conditions of finite-time and fixed-time (integral) input-to-state stability are derived by finding suitable Lyapunov functions. The proposed stability conditions are constructive, which is demonstrated in several applications.

中文翻译：

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机械系统的有限/固定时间 ISS-Lyapunov 函数设计

对于通过势能梯度和耗散项定义的规范形式的机械系统，有限时间和固定时间（积分）输入到状态稳定性的条件是通过找到合适的李雅普诺夫函数推导出来的。所提出的稳定性条件是建设性的，这在几个应用中得到了证明。