Admissible Observation Operators of Abstract Linear Viscoelastic Systems

• 成果类型: Article
• 署名作者: Chen, Jian-Hua; Zhou, Hua-Cheng; Han, Zhong-Jie
• 署名单位: Hunan University of Science & Technology; Central South University; Tianjin University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3408050
• 发表日期: 2024
• 页码: 8449-8464
• 关键词: Convolution; mathematical models; strain; kernel; Hilbert space; Young's modulus; HISTORY; Dafermos's approach; infinite-time admissibility; linear viscoelasticity; memory kernel; operator semigroups

摘要

In this article, we study a class of integro-differential equation systems with observations in the abstract setting of Hilbert spaces, which fit the second-order integro-differential equation governing the dynamics in isotropic linear viscoelastic materials. Our focus is on infinite-time admissibility of the system observation operators, and sufficient conditions are established using two operator semigroup approaches. An illustrative example is given.