Applied Mathematics and Mechanics

, Volume 12, Issue 11, pp 1057–1063 | Cite as

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
Article
  • 37 Downloads

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 and the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stability of robot has been presented by applying the theorem in this paper, which is closer to reality.

Key words

stability nonautonomous system frequently-acting perturbation state transition matrix robot 

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References

  1. [1]
    Zhang Shu-shun Theorem of the stability of linear nonautonomous system under the frequently-acting perturbation,Applied Mathematics and Mechanics,7 (2) (1986), 185–187.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Zhang Shu-shun, Theorem of the stability of linear nonautonomous system under the frequently-acting perturbation (continuation).A collections of Treatises of the First National Scholastic Conference of Stability of Motion and Vibration,1 (1986).Google Scholar
  3. [3]
    Malkin, I. G.,The Theory of Stability of Motion, Gostekhizdat, Moscow, Chap. 6, § 74 (1952).Google Scholar
  4. [4]
    Yoram, Koren,Robotics for Engineers, McGraw-Hill, Book Company, Inc. (1985), 54–81.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1991

Authors and Affiliations

  • Zhang Shu-shun
    • 1
  1. 1.Haerbin Shipbuilding Engineering InstituteHaerbin

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