| 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. |
| 关键词: Lyapunov stability, nonconvex differential inclusions, generalized invariance principle, attraction |
| DOI： |
| Received:March 03, 2016Revised:April 20, 2016 |
| 基金项目: |
|
| Lyapunov stability and generalized invariance principle for nonconvex differential inclusions |
| S. Liang,X. Zeng,Y. Hong |
| (Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences) |
| Abstract: |
| 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. |
| Key words: Lyapunov stability, nonconvex differential inclusions, generalized invariance principle, attraction |
