BOUNDARY STABILIZATION OF A 1-D WAVE EQUATION WITH IN-DOMAIN ANTIDAMPING

被引：149

作者：

Smyshlyaev, Andrey ^{[1
]}

Cerpa, Eduardo ^{[2
]}

Krstic, Miroslav ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA

[2] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2010年 / 48卷 / 06期

关键词：

wave equation; stabilization; backstepping; PARTIAL-DIFFERENTIAL EQUATIONS; FEEDBACK STABILIZATION; DECAY; CONTROLLABILITY; OPERATORS; SYSTEMS;

D O I：

10.1137/080742646

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the problem of boundary stabilization of a 1-D (one-dimensional) wave equation with an internal spatially varying antidamping term. This term puts all the eigenvalues of the open-loop system in the right half of the complex plane. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate. For plants with constant parameters the control gains are found in closed form. Our design also produces a new Lyapunov function for the classical wave equation with passive boundary damping.

引用

页码：4014 / 4031

页数：18

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