This paper addresses the dynamic output feedback guaranteed cost control problem of a
class of time-delay systems where the state and output contain interval nondifferentiable
time-varying delays. The proposed controller uses only the delayed output measurement
to stabilize the closed-loop system and guarantee an adequate level of system performance.
By constructing a set of multiple Lyapunov–Krasovskii functionals which include
triple-integral terms, a new criterion for the existence of dynamic output feedback guaranteed
cost controllers is established and expressed in terms of linear matrix inequality (LMI).
A numerical example is given to illustrate the obtained results.

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