We give new criteria for weak and strong invariant closed sets for differential inclusions in \(\mathbb {R}^{n}\), and which are simultaneously governed by Lipschitz Cusco mapping and by maximal monotone operators. Correspondingly, we provide different characterizations for the associated strong Lyapunov functions and pairs. The resulting conditions only depend on the data of the system, while the invariant sets are assumed to be closed, and the Lyapunov pairs are assumed to be only lower semi-continuous.

中文翻译：

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最大单调算子的Lipschitz Cusco扰动的微分包含的Lyapunov稳定性

我们为\（\ mathbb {R} ^ {n} \）中的微分包含给出了弱和强不变封闭集的新准则，这些准则同时由Lipschitz Cusco映射和最大单调算子控制。相应地，我们为关联的强大Lyapunov函数和对提供了不同的表征。生成的条件仅取决于系统的数据，而假定不变集是封闭的，而Lyapunov对仅假定为下半连续。