The Theorem of the Stability of Linear Nonautonomous Systems under the Frequently-Acting Perturbation and Its Application in the Stability Analysis of Robot

Zhang Shu-shun

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(11): 989-995

Zhang Shu-shun. The Theorem of the Stability of Linear Nonautonomous Systems under the Frequently-Acting Perturbation and Its Application in the Stability Analysis of Robot[J]. Applied Mathematics and Mechanics, 1991, 12(11): 989-995.

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The Theorem of the Stability of Linear Nonautonomous Systems under the Frequently-Acting Perturbation and Its Application in the Stability Analysis of Robot

Zhang Shu-shun

Haerbin Shipbuilding Engineering Institute, Haerbin

Received Date: 1989-08-26
Publish Date: 1991-11-15

Abstract

Abstract

The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of [1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality.
- stability,
- nonautonomous system,
- frequently-acting perturbation,
- state transition matrix,
- robot

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References(4)

References

[1]	张书顺,非定常线性系统在经常作用干扰下的稳定性定理.应用学数和力学,7(2) (1986),189-171.
[2]	张书顺,非定常线性系统在经常作用千扰下的稳定性定理(续),全国首届运动稳定性与振动学术会议(1986)论文集,第一集.
[3]	Малкии Н.Г.,Теорца Усmоцчцзосmц Дбцженця,Гостехиздат(1952):中译本,解伯民等译.《运动稳定性理论》.科学出版社(1958).
[4]	Koren, Yoram, Robotics for Engineers, McGraw-Hill Inc, (1985), 54-81.