International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 2012
Volume 22 - 2012

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

Mai Viet Thuan, Vu Ngoc Phat, Hieu Trinh

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 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.

observer-based feedback control, interval time-varying delay, linear matrix inequalities, Lyapunov–Krasovskii functionals, exponential stability