Variable structure observer design for a class of uncertain systems with a time-varying delay

Wen-Jeng Liu

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 3, page 575-583
  • ISSN: 1641-876X

Abstract

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Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

How to cite

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Wen-Jeng Liu. "Variable structure observer design for a class of uncertain systems with a time-varying delay." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 575-583. <http://eudml.org/doc/244057>.

@article{Wen2012,
abstract = {Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.},
author = {Wen-Jeng Liu},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {variable structure observer; invariance property; generalized matrix inverse approach},
language = {eng},
number = {3},
pages = {575-583},
title = {Variable structure observer design for a class of uncertain systems with a time-varying delay},
url = {http://eudml.org/doc/244057},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Wen-Jeng Liu
TI - Variable structure observer design for a class of uncertain systems with a time-varying delay
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 3
SP - 575
EP - 583
AB - Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.
LA - eng
KW - variable structure observer; invariance property; generalized matrix inverse approach
UR - http://eudml.org/doc/244057
ER -

References

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