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1 International Journal of Applied Mathematics and Computer Science

1 2012

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

Thuan M. V., Phat V. N., Trinh H.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 4

921-927

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 \alfa-convergence rate. The design of an observer based 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.