使用同伦算法验证单调系统的稳定性
Stability verification for monotone systems using homotopy algorithms
AI总结：
本文提出一种数值方法，通过寻找在分量序下映射点严格小于原点的点，来验证单调离散时间动力系统的吸引性，并应用于大规模系统稳定性理论中的广义小增益条件的数值验证。
摘要：
非负象限上的单调自映射诱导出一个在同一象限上演化的单调离散时间动力系统。如果关于该系统原点是吸引的，则必存在点，其在单调映射下的像在分量偏序下严格小于原点。本文展示了如何数值地找到这样的点，从而得到一种计算包含在吸引域中的序区间的方法，在该区间内单调映射本质上起压缩作用。一个重要应用是数值验证大规模系统稳定性理论中出现的所谓广义小增益条件。
英文摘要：
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under the monotone map is strictly smaller than the original point, in the component-wise partial ordering. Here it is shown how such points can be found numerically, leading to a recipe to compute order intervals that are contained in the region of attraction and where the monotone map acts essentially as a contraction. An important application is the numerical verification of so-called generalized small-gain conditions that appear in the stability theory of large-scale systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
