Boundary stabilization of an anti-stable wave equation with in-domain anti-damping

Author

Smyshlyaev, Andrey ; Cerpa, Eduardo ; Krstic, Miroslav

Author_Institution

Dept. of Mech. & Aerosp. Eng., Univ. of California at San Diego, La Jolla, CA, USA

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

2363

Lastpage

2368

Abstract

We consider the problem of boundary stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping 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.

Keywords

Lyapunov methods; asymptotic stability; closed loop systems; damping; eigenvalues and eigenfunctions; feedback; open loop systems; wave equations; 1D wave equation; Lyapunov function; antistable wave equation; backstepping method; boundary stabilization; closed-loop system; control gain; eigenvalues; exponential stability; feedback law; in-domain antidamping; open-loop system; passive boundary damping; Aerospace engineering; Asymptotic stability; Backstepping; Damping; Eigenvalues and eigenfunctions; Feedback; Lyapunov method; Open loop systems; Partial differential equations; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400674

Filename

5400674