A Model Reduction Approach for Discrete-Time Coupled Systems With Input Delays via Bivariate Fundamental Matrices

• 成果类型: Article
• 署名作者: Wu, Ai-Guo; Shen, Shi-Long; Zhang, Jie; Mei, Jie
• 署名单位: Harbin Institute of Technology; Southern University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3633355
• 发表日期: 2026
• 关键词: DIFFERENTIAL-DIFFERENCE EQUATIONS; stability analysis; VARYING SYSTEMS; linear-systems; stabilization; state; Positivity

摘要

In this article, the model reduction approach is investigated for discrete-time linear coupled systems with input delays. For this purpose, a new class of fundamental matrices is presented for state response analysis of this kind of systems. In order to characterize the effect of all initial values, this new fundamental matrix is defined in terms of two independent variables, and thus is called the bivariate fundamental matrix. Besides, some interesting properties of bivariate fundamental matrices are provided. According to the derived state response expression, two particular changes of state variables are constructed to transform the considered coupled input-delayed system into an input-delay-free system. Further, a state feedback controller is designed to stabilize the considered system based on the obtained input-delay-free system. In addition, by using the properties of bivariate fundamental matrices, the characteristic equation of the resulting closed-loop system under the designed controller is explored. The derived results reveal that the designed control law can entirely compensate the input delays, and thus can stabilize the considered system.