Article

Circuits, Systems and Signal Processing

, Volume 5, Issue 1, pp 153-169

Multiple time scales for nonlinear systems

  • R. Silva-MadrizAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of CaliforniaThe Electronics Research Laboratory, University of California
  • , S. S. SastryAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of CaliforniaThe Electronics Research Laboratory, University of California

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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.