关于微分包含的约简与李雅普诺夫稳定性
On reduction of differential inclusions and Lyapunov stability
AI总结：
本文研究了利用局部Lipschitz正则函数来识别并移除微分包含中不可行方向的方法，从而得到更小的集值映射，并发展出一种广义导数，用于局部Lipschitz候选李雅普诺夫函数的方向分析，从而得到更宽松的李雅普诺夫稳定性定理等结论。
摘要：
在本文中，局部Lipschitz、正则函数被用来识别并移除定义微分包含的集值映射中的不可行方向。所得到的约简集值映射在集包含意义上比原集值映射更小。由此定义的约简微分包含被用来发展一种广义的导数，用于局部Lipschitz候选李雅普诺夫函数在集值映射方向上的导数。所发展的广义导数能够产生更宽松的李雅普诺夫稳定性定理、不变性定理、类似不变性结果以及Matrosov定理。包含的示例展示了所发展理论的实用性。
英文摘要：
In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory.
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