中文摘要：

这份报纸学习 nonconvex 的一个班的系统稳定性问题微分包括。起初，基本稳定性结果被优点获得局部地， Lipschitz 连续 Lyapunov 工作。而且，一个概括不变性原则和相关吸引力条件被建议并且证明了由于凸状的缺席克服技术困难。在技术分析，新奇珍视集合的衍生物被建议处理 nonsmooth 系统和 nonsmooth Lyapunov 功能。另外，获得的结果与在有常规 Lyapunov 功能的凸的微分包括的情况中的存在的一致。最后，解说性的例子被给显示出方法的有效性。

英文摘要：

This paper studies the system stability problems of a class of nonconvex differential inclusions. At first, a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions. Moreover, a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity. In the technical analysis, a novel set-valued derivative is proposed to deal with nonsmooth systems and nonsmooth Lyapunov functions. Additionally, the obtained results are consistent with the existing ones in the case of convex differential inclusions with regular Lyapunov functions. Finally, illustrative examples are given to show the effectiveness of the methods.