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Multiple time scales for nonlinear systems

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Abstract

In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form

$$\dot x = A( \in )x$$

(cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.

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References

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, 94720, Berkeley, California, USA

    R. Silva-Madriz & S. S. Sastry

  2. The Electronics Research Laboratory, University of California, 94720, Berkeley, California, USA

    R. Silva-Madriz & S. S. Sastry

Authors
  1. R. Silva-Madriz
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  2. S. S. Sastry
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Additional information

This research was supported in part by NASA under grant NAG 2-243.

All eigenvalues ofA 0 (ε) are in the open left half plane except possibly some at the origin. Further, there are no generalized eigenvectors associated with the zero eigenvalue.

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Silva-Madriz, R., Sastry, S.S. Multiple time scales for nonlinear systems. Circuits Systems and Signal Process 5, 153–169 (1986). https://doi.org/10.1007/BF01600193

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  • DOI: https://doi.org/10.1007/BF01600193

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