Observer design for a class of nonlinear discrete-time systems with time-delay

Yali Dong; Jinying Liu; Shengwei Mei

Kybernetika (2013)

  • Volume: 49, Issue: 2, page 341-358
  • ISSN: 0023-5954

Abstract

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The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.

How to cite

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Dong, Yali, Liu, Jinying, and Mei, Shengwei. "Observer design for a class of nonlinear discrete-time systems with time-delay." Kybernetika 49.2 (2013): 341-358. <http://eudml.org/doc/260625>.

@article{Dong2013,
abstract = {The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.},
author = {Dong, Yali, Liu, Jinying, Mei, Shengwei},
journal = {Kybernetika},
keywords = {observer design; stability; time-delay; differential mean value theory; Lyapunov–Krasovskii functional; observer design; stability; time-delay; differential mean value theory; Lyapunov-Krasovskiĭ functional},
language = {eng},
number = {2},
pages = {341-358},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Observer design for a class of nonlinear discrete-time systems with time-delay},
url = {http://eudml.org/doc/260625},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Dong, Yali
AU - Liu, Jinying
AU - Mei, Shengwei
TI - Observer design for a class of nonlinear discrete-time systems with time-delay
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 2
SP - 341
EP - 358
AB - The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.
LA - eng
KW - observer design; stability; time-delay; differential mean value theory; Lyapunov–Krasovskii functional; observer design; stability; time-delay; differential mean value theory; Lyapunov-Krasovskiĭ functional
UR - http://eudml.org/doc/260625
ER -

References

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