关于$H_\infty$控制中出现的耗散不等式的连续、Lipschitz和可微存储函数之间的间隙的注记
Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in $H_\infty$ control
摘要：
本文讨论H ∞控制中的Hamilton-Jacobi不等式解的正则性。通过明确的反例说明了连续解的存在性与局部Lipschitz（正定和真）解的存在性以及Lipschitz解与连续可微解的存在性之间存在着差距.另一方面，它表明，它总是可以平滑的解决方案，只要允许增益的无限小的增加。
英文摘要：
This paper deals with the regularity of solutions of the Hamilton-Jacobi Inequality which arises in H-infinity control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive definite and proper) solutions, and between Lipschitz and continuously differentiable ones. On the other hand, it is shown that it is always possible to smooth-out solutions, provided that an infinitesimal increase in gain is allowed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
