论文标题
$ l^{2} $ norm
Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm
论文作者
论文摘要
在本文中，我们研究了$ l^{2} $半线性规范的全球指数稳定性，当源术语和非线性边界条件是Lipschitz时，有界域上的双曲线系统的全球稳定性。我们表现出两个足够的稳定条件：内部条件和边界条件。当源项是非本地的时，此结果也成立。最后，我们通过将其扩展到$ l^{2} $ norm中的内部和边界干扰中的全局输入到状态稳定性来表明其鲁棒性。
In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear $1$-$d$ hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient stability conditions: an internal condition and a boundary condition. This result holds also when the source term is nonlocal. Finally, we show its robustness by extending it to global Input-to State Stability in the $L^{2}$ norm with respect to both interior and boundary disturbances.
