Uniform stabilization of a wave equation with partial Dirichlet delayed control. (English) Zbl 1443.35092
Authors’ abstract: We consider the uniform stabilization of some high-dimensional wave equations with partial Dirichlet delayed control. Herein we design a parameterization feedback controller to stabilize the system. This is a new approach of controller design which overcomes the difficulty in stability analysis of the closed-loop system. The detailed procedure is as follows: At first, we rewrite the system with partial Dirichlet delayed control into an equivalence cascaded system of a transport equation and a wave equation, and then we construct an exponentially stable target system; Further, we give the form of the parameterization feedback controller. To stabilize the system under consideration, we choose some appropriate kernel functions and define a bounded inverse linear transformation such that the closed-loop system is equivalent to the target system. Finally, we obtain the stability of closed-loop system by the stability of target system.
Reviewer: Kaïs Ammari (Monastir)
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35L05 | Wave equation |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93D15 | Stabilization of systems by feedback |
| 35G15 | Boundary value problems for linear higher-order PDEs |
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