Stabilization of Linear Systems with Two Time Scales

  • Vasile Dragan
  • Aristide Halanay
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

In many situations the mathematical models used to describe the object to be regulated exhibit in a natural way several time scales. To illustrate this idea we shall consider only two examples. In the mathematical modeling of a synchronous machine, the evolution of the mechanical part is much slower than the one corresponding to the electrical one.

Keywords

Lime Lution Dinates 

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Notes and References

  1. There are several sources for general aspects concerning singularly perturbed systems [43], [50] and their references. Separation of time scales can be found in [3], but was used much earlier in [27]. A general survey concerning the use of singular perturbations in control is [42], where an extended list of references is given. A previous survey is also [41). An extended list of references is given in [57]. The book [37] contains a nice chapter on singular perturbations, where the time interval is also [0, ∞). The results in Section 3.3 and Section 3.4 are based on [8] and [12], respectively.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Vasile Dragan
    • 1
  • Aristide Halanay
    • 1
  1. 1.Institute of Mathematics of the Romanian AcademyBucharestRomania

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