On the Stability of Discontinuous Systems via Vector Liapunov Functions

MU Xiao-wu; CHENG Gui-fang; DING Zhi-shuai

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MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.

Citation:

MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.

Citation:

MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.

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On the Stability of Discontinuous Systems via Vector Liapunov Functions

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China

Received Date: 2006-07-04
Rev Recd Date: 2007-10-12
Publish Date: 2007-12-15

Abstract

Abstract

The stability of systems with discontinuous right-hand side (with solutions in Filippov's sense) via locally Lipschitz continuous and regular vector Liapunov functions are discussed. A new type of "set-valued derivative" of vector Liapunov functions was introduced, some generalized comparison principles on discontinuous systems were shown. Furthermore Liapunov stability theory was developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Liapunov functions.
- Filippov solutions,
- comparison principles,
- stability,
- vector Liapunov functions,
- discontinuous systems

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References(13)

References

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