In-Domain Stabilization of Block Diagonal Infinite-Dimensional Systems With Time-Varying Input Delays

• 成果类型: Article
• 署名作者: Lhachemi, Hugo; Prieur, Christophe; Shorten, Robert
• 署名单位: Universite Paris Saclay; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Imperial College London; University College Dublin
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3059103
• 发表日期: 2021
• 页码: 6017-6024
• 关键词: Delays; Mathematical model; control design; Time-varying systems; Symmetric matrices; Generators; stability analysis; Delayed distributed actuation; partial differential equations (PDEs); predictor feedback law

摘要

This article is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated linear time invariant (LTI) model capturing the unstable dynamics of the original infinite-dimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered.