Abstract
Stabilization of linear parabolic boundary control systems is studied. The boundary control system is composed of a system of linear differential operators (ℒ, τ) in a bounded domain with the smooth boundary. A significant feature of the paper is that, while ℒ being a standard elliptic operator, τ characterizes the boundary condition partly of the Dirichlet type and partly of the generalized Neumann type. We present a new algebraic approach and show that the stabilization is achieved under the standard controllability and observability conditions associated with the system.
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Nambu, T. An Algebraic Method of Stabilization for a Class of Boundary Control Systems of Parabolic Type. Journal of Dynamics and Differential Equations 13, 59–85 (2001). https://doi.org/10.1023/A:1009040414659
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DOI: https://doi.org/10.1023/A:1009040414659