Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

Shu Liang; Xianlin Zeng; Yiguang Hong

doi:10.1007/s11768-016-6037-2

Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

Shu Liang, Xianlin Zeng, Yiguang Hong^*

^*Corresponding author for this work

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	140-150
Number of pages	11
Journal	Control Theory and Technology
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s11768-016-6037-2
Publication status	Published - 1 May 2016
Externally published	Yes

Keywords

Lyapunov stability
attraction
generalized invariance principle
nonconvex differential inclusions

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10.1007/s11768-016-6037-2

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title = "Lyapunov stability and generalized invariance principle for nonconvex differential inclusions",

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.",

keywords = "Lyapunov stability, attraction, generalized invariance principle, nonconvex differential inclusions",

author = "Shu Liang and Xianlin Zeng and Yiguang Hong",

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T1 - Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

AU - Liang, Shu

AU - Zeng, Xianlin

AU - Hong, Yiguang

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Lyapunov stability

KW - attraction

KW - generalized invariance principle

KW - nonconvex differential inclusions

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VL - 14

SP - 140

EP - 150

JO - Control Theory and Technology

JF - Control Theory and Technology

IS - 2

ER -

Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

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Keywords

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