论文标题
沿解决方案的标量函数非降低的必要条件
Necessary and Sufficient Conditions for the Nonincrease of Scalar Functions Along Solutions to Constrained Differential Inclusions
论文作者
论文摘要
在本文中，我们提出了标量函数的必要条件，即沿着具有状态限制的一般差分包含物的解决方案进行非进化。确定函数是否不渗透的问题出现在稳定性和安全性研究中，通常分别使用Lyapunov和屏障功能。本文的结果呈现无限条件，这些条件不需要有关系统解决方案的任何知识。提供了在考虑的标量函数的不同规律性属性下的结果。这包括标量函数较低的半连续，局部Lipschitz和常规或不断差异。
In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing appears in the study of stability and safety, typically using Lyapunov and barrier functions, respectively. The results in this paper present infinitesimal conditions that do not require any knowledge about the solutions to the system. Results under different regularity properties of the considered scalar function are provided. This includes when the scalar function is lower semicontinuous, locally Lipschitz and regular, or continuously differentiable.
