Boundary stabilization of a 1-D wave equation with in-domain antidamping

Andrey Smyshlyaev, Eduardo Cerpa, Miroslav Krstic

Research output: Contribution to journalArticle

101 Citations (Scopus)


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. © 2010 Societ y for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)4014-4031
Number of pages18
JournalSIAM Journal on Control and Optimization
Publication statusPublished - 7 Oct 2010

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