Stabilization of second-order systems by non-linear feedback

Paweł Skruch

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 4, page 455-460
  • ISSN: 1641-876X

Abstract

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A stabilization problem of second-order systems by non-linear feedback is considered. We discuss the case when only position feedback is available. The non-linear stabilizer is constructed by placing actuators and sensors in the same location and by using a parallel compensator. The stability of the closed-loop system is proved by LaSalle's theorem. The distinctive feature of the solution is that no transformation to a first-order system is invoked. The results of analytic and numerical computations are included to verify the theoretical analysis and the mathematical formulation.

How to cite

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Skruch, Paweł. "Stabilization of second-order systems by non-linear feedback." International Journal of Applied Mathematics and Computer Science 14.4 (2004): 455-460. <http://eudml.org/doc/207710>.

@article{Skruch2004,
abstract = {A stabilization problem of second-order systems by non-linear feedback is considered. We discuss the case when only position feedback is available. The non-linear stabilizer is constructed by placing actuators and sensors in the same location and by using a parallel compensator. The stability of the closed-loop system is proved by LaSalle's theorem. The distinctive feature of the solution is that no transformation to a first-order system is invoked. The results of analytic and numerical computations are included to verify the theoretical analysis and the mathematical formulation.},
author = {Skruch, Paweł},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {non-linear feedback; second-order system; stability theory},
language = {eng},
number = {4},
pages = {455-460},
title = {Stabilization of second-order systems by non-linear feedback},
url = {http://eudml.org/doc/207710},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Skruch, Paweł
TI - Stabilization of second-order systems by non-linear feedback
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 4
SP - 455
EP - 460
AB - A stabilization problem of second-order systems by non-linear feedback is considered. We discuss the case when only position feedback is available. The non-linear stabilizer is constructed by placing actuators and sensors in the same location and by using a parallel compensator. The stability of the closed-loop system is proved by LaSalle's theorem. The distinctive feature of the solution is that no transformation to a first-order system is invoked. The results of analytic and numerical computations are included to verify the theoretical analysis and the mathematical formulation.
LA - eng
KW - non-linear feedback; second-order system; stability theory
UR - http://eudml.org/doc/207710
ER -

References

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  2. Diwekar A.M. and Yedavalli R.K. (1999): Stability of matrix second-order systems: New conditions and perspectives. - IEEE Trans. Automat. Contr., Vol. 44, No. 9, pp. 1773-1777. Zbl0958.93081
  3. Klamka J. (1990): Controllability of Dynamic Systems. - Warsaw: Polish Scientific Publishers, (in Polish). Zbl0736.93005
  4. Kobayashi T. (2001): Low gain adaptive stabilization of undamped second order systems. - Arch. Contr. Sci., Vol. 11 (XLVII), Nos. 1-2, pp. 63-75. Zbl1151.93423
  5. LaSalle J. and Lefschetz S. (1966): Stability by Liapunov's Direct Method with Applications. - Warsaw: WNT, (in Polish). 
  6. Mitkowski W. (1991): Stabilization of Dynamic Systems. - Warsaw: Polish Scientific Publishers, (in Polish). Zbl0686.93072
  7. Mitkowski W. (2003): Dynamic feedback in LC ladder network. - Bulletin of the Polish Academy of Sciences, Technical Sciences, Vol. 51, No. 2, pp. 173-180. Zbl1053.93036

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