Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems

Keqin Gu

Kybernetika (2001)

  • Volume: 37, Issue: 4, page [479]-504
  • ISSN: 0023-5954

Abstract

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This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov–Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.

How to cite

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Gu, Keqin. "Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems." Kybernetika 37.4 (2001): [479]-504. <http://eudml.org/doc/33547>.

@article{Gu2001,
abstract = {This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov–Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.},
author = {Gu, Keqin},
journal = {Kybernetika},
keywords = {time-delay system; Lyapunov-Krasovskii functional; multiple delays; time-delay system; Lyapunov-Krasovskii functional; multiple delays},
language = {eng},
number = {4},
pages = {[479]-504},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems},
url = {http://eudml.org/doc/33547},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Gu, Keqin
TI - Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 4
SP - [479]
EP - 504
AB - This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov–Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.
LA - eng
KW - time-delay system; Lyapunov-Krasovskii functional; multiple delays; time-delay system; Lyapunov-Krasovskii functional; multiple delays
UR - http://eudml.org/doc/33547
ER -

References

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