A Sufficient Condition for k-Contraction of the Series Connection of Two Systems

• 成果类型: Article
• 署名作者: Ofir, Ron; Margaliot, Michael; Levron, Yoash; Slotine, Jean-Jacques
• 署名单位: Technion Israel Institute of Technology; Tel Aviv University; Massachusetts Institute of Technology (MIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3177715
• 发表日期: 2022
• 页码: 4994-5001
• 关键词: Compound matrices; contracting systems; series connections; Thomas' cyclically symmetric attractor

摘要

The flow of an n-dimensional k-contracting system, with k is an element of {1, ..., n}, contracts k-dimensional parallelotopes. For k = 1, this reduces to a standard contracting system. One reason for the usefulness of 1-contracting systems is that many interconnections of contracting subsystems yield an overall 1-contracting system. Here, we derive a new sufficient condition guaranteeing that the system obtained from the series interconnection of two subsystems is k-contracting. This is based on a new formula for the kth multiplicative and additive compounds of a block-diagonal matrix (BDM), which may be of independent interest. As an application, we find conditions guaranteeing that 2-contracting systems with an exponentially decaying input retain the well-ordered behavior of time-invariant 2-contracting systems.