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math.AP2021
Fredholm transformation on Laplacian and rapid stabilization for the heat equation
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption…
math.OC2021
PI controllers for the general Saint-Venant equations
Amaury Hayat
We study the exponential stability in the norm of the nonlinear Saint-Venant (or shallow water) equations with arbitrary friction and slope using a single Proportional-Inte…
math.AP2021★ 20 cited
Stabilization of the linearized water tank system
Jean-Michel Coron, Amaury Hayat, Shengquan Xiang +1
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 distrib…