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Applied Mathematics and Mechanics

, Volume 12, Issue 7, pp 717–725 | Cite as

The theorem of the stability of nonlinear nonautonomous systems under the frequently-acting perturbation —Liapunov's indirect method

  • Zhang Shu-shun
  • Shang Da-zhang
Article
  • 19 Downloads

Abstract

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

Key words

nonautonomous system frequently-acting perturbation uniformly asymptotical stability state transition matrix 

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References

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    Vidyasagar, M.,Nonlinear Systems Analysis, Prentice-Hall, Inc., Englowood Cliffs, New Jersey (1978), 179–181, 71.Google Scholar
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    Wang Zhao-lin and Zheng Fan-cai, Method of large-scale system and analysis of three-axis stability of system partially filled with liquid,Journal of Mechanics,20, 2 (1988), 49–50.Google Scholar

Copyright information

© Shanghai University of Technology 1991

Authors and Affiliations

  • Zhang Shu-shun
    • 1
  • Shang Da-zhang
    • 1
  1. 1.Haerbin Shipbuilding Engineering InstituteHaerbin

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