Linear passive systems and maximal monotone mappings

• 成果类型: Article
• 署名作者: Camlibel, M. K.; Schumacher, J. M.
• 署名单位: University of Groningen; Dogus University; Tilburg University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0945-7
• 发表日期: 2016
• 页码: 397-420
• 关键词: Absolute stability; DYNAMICAL-SYSTEMS; uniqueness

摘要

This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is passive and the static relation is maximal monotone. Based on the classical results on such differential inclusions, we conclude that such interconnections are well-posed in the sense of existence and uniqueness of solutions. Finally, we investigate conditions which guarantee well-posedness but are weaker than passivity.