Observer-based controller design of time-delay systems with an interval time-varying delay

Mai Viet Thuan; Vu Ngoc Phat; Hieu Trinh

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 4, page 921-927
  • ISSN: 1641-876X

Abstract

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This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

How to cite

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Mai Viet Thuan, Vu Ngoc Phat, and Hieu Trinh. "Observer-based controller design of time-delay systems with an interval time-varying delay." International Journal of Applied Mathematics and Computer Science 22.4 (2012): 921-927. <http://eudml.org/doc/244531>.

@article{MaiVietThuan2012,
abstract = {This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.},
author = {Mai Viet Thuan, Vu Ngoc Phat, Hieu Trinh},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {observer-based feedback control; interval time-varying delay; linear matrix inequalities; Lyapunov-Krasovskii functionals; exponential stability},
language = {eng},
number = {4},
pages = {921-927},
title = {Observer-based controller design of time-delay systems with an interval time-varying delay},
url = {http://eudml.org/doc/244531},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Mai Viet Thuan
AU - Vu Ngoc Phat
AU - Hieu Trinh
TI - Observer-based controller design of time-delay systems with an interval time-varying delay
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 4
SP - 921
EP - 927
AB - This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.
LA - eng
KW - observer-based feedback control; interval time-varying delay; linear matrix inequalities; Lyapunov-Krasovskii functionals; exponential stability
UR - http://eudml.org/doc/244531
ER -

References

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