This paper deals with the problem of optimal guaranteed cost control for
linear systems with interval time-varying delayed state and control. The time delay is
assumed to be a continuous function belonging to a given interval, but not necessary
to be differentiable. A linear–quadratic cost function is considered as a performance
measure for the closed-loop system. By constructing a set of augmented Lyapunov–
Krasovskii functional combined with Newton–Leibniz formula, a guaranteed cost
controller design is presented and sufficient conditions for the existence of a guaranteed
cost state-feedback for the system are given in terms of linear matrix inequalities
(LMIs). Numerical examples are given to illustrate the effectiveness of the obtained
result.

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