Stabilization of the linearized water tank system
In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar …
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Internal rapid stabilization of a linear transport equation with a scalar feedback
We use a variant of the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0,L), by controlling the scalar amplitude of a piecewise …
Finite-time internal stabilization of a 1-D linear transport equation
We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar control. We prove that if the system is controllable in a periodic Sobolev space of …
Internal Controllability of Systems of Semilinear Coupled One-Dimensional Wave Equations with One Control
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this …