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arXiv 2303.045632023-03math.APmath.FAmath.OC

双线性反馈系统的输入到状态稳定性

Input-to-state stability for bilinear feedback systems

René Hosfeld, Birgit Jacob, Felix Schwenninger, Marius Tucsnak

备注：: 22 pages

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AI总结：

本文证明了具有双线性反馈的无穷维系统在小初始条件下的输入到状态稳定性，并将结果应用于粘性 Burger 方程、Schrödinger 方程、Navier--Stokes 系统及半线性波方程的控制版本。

摘要：

本文证明了具有双线性反馈的无穷维系统关于小初始条件和输入函数的输入到状态稳定性估计。我们将所得结果应用于带 Dirichlet 边界条件的粘性 Burger 方程、Schrödinger 方程、Navier--Stokes 系统及半线性波方程的控制版本。

英文摘要：

Input-to-state stability estimates with respect to small initial conditions and input functions for infinite-dimensional systems with bilinear feedback are shown. We apply the obtained results to controlled versions of a viscous Burger equation with Dirichlet boundary conditions, a Schrödinger equation, a Navier--Stokes system and a semilinear wave equation.

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