# 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

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topMai 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 -

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