Geodesic
Observer-based controller design of time-delay systems with an interval time-varying delay
International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 921-927.

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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 -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.
Keywords: observer based feedback control, interval time-varying delay, linear matrix inequality, Lyapunov-Krasovskii functional, exponential stability
Mots-clés : sprzężenie zwrotne, opóźnienie czasowo zależne, liniowa nierówność macierzowa, funkcjonał Lapunowa-Krasowskiego, stabilność wykładnicza 
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Thuan, M. V.; Phat, V. N.; Trinh, H. Observer-based controller design of time-delay systems with an interval time-varying delay. International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 921-927. http://geodesic.mathdoc.fr/item/IJAMCS_2012_22_4_a10/

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