关于混合单调性的充分条件
On sufficient conditions for mixed monotonicity
AI总结：
本文探讨了混合单调性系统的定义关系，提出两种更通用的充分条件，揭示了混合单调性是一种普遍性质，并讨论了其计算实用性。
摘要：
混合单调系统是一个重要的非线性系统类别，最近在基于抽象的控制设计领域引起了关注。文献中存在略有不同的定义，一般情况下验证系统的混合单调性仍是一个挑战。本文首先澄清了现有混合单调系统定义之间的关系，然后给出了定义在欧几里得空间上的混合单调函数的两个充分条件。这些充分条件比现有控制文献中的更通用，表明混合单调性是一种非常普遍的性质。一些讨论提供了所提出充分条件的计算实用性的见解。
英文摘要：
Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to verify mixed monotonicity of a system in general. In this paper, we first clarify the relation between different existing definitions of mixed monotone systems, and then give two sufficient conditions for mixed monotone functions defined on Euclidean space. These sufficient conditions are more general than the ones from the existing control literature, and they suggest that mixed monotonicity is a very generic property. Some discussions are provided on the computational usefulness of the proposed sufficient conditions.
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