This paper considers the problem of designing an observer-based output feedback
controller to exponentially stabilize a class of linear systems with interval timevarying
delay in the state vector. The time-varying 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 its lower bound be zero. By constructing a set of
Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delaydependent
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
illustrated the design procedure.

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