非定常线性系统在经常作用干扰下的稳定性定理及其在机器人动态稳定性分析中的应用
The Theorem of the Stability of Linear Nonautonomous Systems under the Frequently-Acting Perturbation and Its Application in the Stability Analysis of Robot
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摘要: 本文在文献[1]、[2]的基础上,给出并证明了非定常线性系统在经常作用干扰下稳定的充分和必要条件,并推得该系统在李雅普诺夫意义下一致渐近稳定和在经常作用干扰下稳定等价的定理.此外,作者还应用文中的定理,对机器人动态稳定性进行了比较切合实际的分析.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.
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Key words:
- stability /
- nonautonomous system /
- frequently-acting perturbation /
- state transition matrix /
- robot
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[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. -
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