ConferencePaper
Proceedings of the IEEE Conference on Decision and Control  (2009)

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

Smyshlyaev, A; Krstic, M; Cerpa, E

Keywords: systems, stability, equations, decay, complex, waves, laws, loop, parameters, constant, form, boundary, feedback, wave, stabilization, control, classical, eigenvalues, method, damping, lyapunov, gains, backstepping, eigenfunctions, Rate, and, Functions, open, exponential, Closed, (organic), one-dimensional, planes, Back-stepping

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. ©2009 IEEE.

Más información

Título de la Revista: Proceedings of the IEEE Conference on Decision and Control
Editorial: IEEE
Fecha de publicación: 2009
Página de inicio: 2363
Página final: 2368
URL: http://www.scopus.com/inward/record.url?eid=2-s2.0-77950844309&partnerID=q2rCbXpz