Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

被引：3

作者：

Caldeira, Andre F. ^{[1
,2
]}

Prieur, Christophe ^{[3
]}

Coutinho, Daniel ^{[4
]}

Leite, Valter J. S. ^{[5
]}

机构：

[1] Univ Fed Santa Catarina, Grad Program Automat & Syst Engn, POB 476, BR-88040900 Florianopolis, SC, Brazil

[2] Grenoble Image Parole Signal Automat GIPSA Lab, F-38000 Grenoble, France

[3] Univ Grenoble Alpes, GIPSA Lab, Grenoble INP, CNRS, F-38000 Grenoble, France

[4] Univ Fed Santa Catarina, Dept Automat & Syst, POB 476, BR-88040900 Florianopolis, SC, Brazil

[5] CEFET MG, Dept Mechatron Engn, Campus Divinopolis,R Alvares Azevedo 400, BR-35503822 Divinopolis, MG, Brazil

来源：

EUROPEAN JOURNAL OF CONTROL | 2018年 / 43卷

关键词：

Dynamic boundary conditions; Poiseuille flow; Linear hyperbolic systems; Robust control; LMIs;

D O I：

10.1016/j.ejcon.2018.05.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper addresses the boundary control problem of fluid transport in a Poiseuille flow taking the actuator dynamics into account. More precisely, sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to nonlinear quadratic dynamic boundary conditions by means of Lyapunov based techniques. Then, convex optimization problems in terms of linear matrix inequality constraints are derived to either estimate the closed-loop stability region or synthesize a robust control law ensuring the local closed-loop stability while estimating an admissible set of initial states. The proposed results are then applied to application-oriented examples to illustrate local stability and stabilization tools. (C) 2018 European Control Association. Published by Elsevier Ltd. All rights reserved.

引用

页码：46 / 56

页数：11

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