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LOCAL EXPONENTIAL H² STABILIZATION OF A 2 x 2 QUASILINEAR HYPERBOLIC SYSTEM USING BACKSTEPPING.
- Source :
-
SIAM Journal on Control & Optimization . 2013, Vol. 51 Issue 3, p2005-2035. 31p. - Publication Year :
- 2013
-
Abstract
- In this work, we consider the problem of boundary stabilization for a quasilinear 2 x 2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H² exponential stability of the closedloop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type 4 x 4 system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and successive approximations. Once the kernels are computed, the stabilizing feedback law can be explicitly constructed from them. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03630129
- Volume :
- 51
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Control & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 89672435
- Full Text :
- https://doi.org/10.1137/120875739