Distributed sampled-data control of Kuramoto-Sivashinsky equation

被引：62

作者：

Kang, Wen ^{[1
,2
]}

Fridman, Emilia ^{[2
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Automat & Elect Engn, Beijing, Peoples R China

[2] Tel Aviv Univ, Sch Elect Engn, Tel Aviv, Israel

来源：

AUTOMATICA | 2018年 / 95卷

基金：

以色列科学基金会;

关键词：

Sampled-data control; Kuramoto-Sivashinsky equation; Linear matrix inequalities; NONLINEAR DISSIPATIVE SYSTEMS; FINITE DETERMINING PARAMETERS; FEEDBACK-CONTROL; STABILITY; STABILIZATION;

D O I：

10.1016/j.automatica.2018.06.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper is devoted to distributed sampled-data control of nonlinear PDE system governed by 1-D Kuramoto-Sivashinsky equation. It is assumed that N sensors provide sampled in time spatially distributed (either point or averaged) measurements of the state over N sampling spatial intervals. Locally stabilizing sampled-data controllers are designed that are applied through distributed in space shape functions and zero-order hold devices. Given upper bounds on the sampling intervals in time and in space, sufficient conditions ensuring regional exponential stability of the closed-loop system are established in terms of Linear Matrix Inequalities (LMIs) by using the time-delay approach to sampled-data control and Lyapunov-Krasovskii method. As it happened in the case of diffusion equation, the descriptor method appeared to be an efficient tool for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation. An estimate on the domain of attraction is also given. A numerical example demonstrates the efficiency of the results. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：514 / 524

页数：11

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