Strict Lyapunov functionals for nonlinear parabolic partial differential equations
Strict Lyapunov functionals for nonlinear parabolic partial differential equations
复制标题
非线性抛物型偏微分方程的严格李亚普诺夫泛函
DOI：
10.3182/20110828-6-it-1002.01572
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
C. Prieur
中科院分区：
文献类型：
--
作者：
F. Mazenc;C. Prieur
摘要对于一类具有特殊边界条件的偏微分方程，构造了严格的李雅普诺夫泛函。所考虑的偏微分方程是抛物型的，除了扩散项外，还可能包含非线性源项和对流项。边界条件可以是经典的狄利克雷条件，也可以是诺伊曼边界条件或周期性边界条件。的建设依赖于知识的弱李雅普诺夫泛函的非线性源项。严格的李雅普诺夫泛函被用来证明在适当的拓扑结构的框架中的渐近稳定性。此外，当考虑不确定性时，我们构造了严格的李雅普诺夫泛函，使得建立输入-状态稳定（ISS）型鲁棒性成为可能。
Abstract For families of partial differential equations (PDEs) with particular boundary conditions, strict Lyapunov functionals are constructed. The PDEs under consideration are parabolic and, in addition to the diffusion term, may contain a nonlinear source term plus a convection term. The boundary conditions may be either the classical Dirichlet conditions, or the Neumann boundary conditions or a periodic one. The constructions rely on the knowledge of weak Lyapunov functionals for the nonlinear source term. The strict Lyapunov functionals are used to prove asymptotic stability in the framework of an appropriate topology. Moreover, when an uncertainty is considered, our construction of a strict Lyapunov functional makes it possible to establish some robustness properties of Input-to-State Stability (ISS) type.