Sampled-Data Control of 2-D Kuramoto-Sivashinsky Equation

• 成果类型: Article
• 署名作者: Kang, Wen; Fridman, Emilia
• 署名单位: University of Science & Technology Beijing; Tel Aviv University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3070070
• 发表日期: 2022
• 页码: 1314-1326
• 关键词: Two dimensional displays; stability analysis; Mathematical model; Heating systems; sensors; Aerospace electronics; Upper bound; 2-D Kuramoto-Sivashinsky equation; sampled-data control

摘要

This article addresses sampled-data control of 2-D Kuramoto-Sivashinsky equation over a rectangular domain Omega. We suggest to divide the 2-D rectangular Omega into N subdomains, where sensors provide spatially averaged or point state measurements to be transmitted through communication network to the controller. Note that, differently from 2-D heat equation, here, we manage with sampled-data control under point measurements. We design a regionally stabilizing sampled-data controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, we find an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.