Constructive Robust Stabilization by Using Square Wave Dithers: A Time-Delay Approach

• 成果类型: Article
• 署名作者: Zhang, Jin; Fridman, Emilia
• 署名单位: Shanghai University; Tel Aviv University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3230772
• 发表日期: 2023
• 页码: 6307-6314
• 关键词: Averaging; stabilization by fast oscillations; time-delay systems

摘要

The article studies robust stabilization of the second and third-order (with relative degree 3) linear uncertain systems by a fast-varying square wave dither with high frequency 1/epsilon and high gain, where epsilon > 0 is small. In contrast to the existing methods for control by fast oscillations that are all qualitative, we present constructive quantitative results for finding an upper bound on epsilon that ensures the exponential stability. Our method consists of two steps: 1) we construct appropriate coordinate transformations that cancel the high gains and lead to a stable averaged system; 2) we apply the time-delay approach to periodic averaging of the system in new coordinates and derive linear matrix inequalities for finding an upper bound on epsilon. Three numerical examples illustrate the efficiency of the method.