极限环存在性、稳定性和鲁棒性的横向收缩准则
Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle
AI总结：
本文推导了自治系统中轨道稳定极限环存在的微分收缩条件，该条件可表示为逐点线性矩阵不等式，从而可利用凸优化工具（如平方和规划）搜索稳定极限环存在的证书，并将收缩动力学的许多理想性质（如互联下收缩保持）推广到该框架，同时通过引入微分耗散性和横向微分耗散性概念，基于子系统LMI条件建立大规模系统的收缩与横向收缩。
摘要：
本文推导了自治系统中轨道稳定极限环存在的微分收缩条件。该横向收缩条件可表示为逐点线性矩阵不等式（LMI），从而允许使用凸优化工具（如平方和规划）来搜索稳定极限环存在的证书。收缩动力学的许多理想性质被推广到这一框架，包括在一大类互联下收缩的保持。此外，通过引入微分耗散性和横向微分耗散性的概念，可以基于子系统的LMI条件建立大规模系统的收缩和横向收缩。
英文摘要：
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.
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