In this paper, we study the stability problem of a single-degree-of freedom system with delayed position and velocity feedback, which can be found in the modeling of several engineering problems in control and vibration. For this class of delay system, we derive some necessary and sufficient conditions for delay-dependent exponential stability. These conditions determine a region in the feedback gains space for assuring the delay-dependent exponential stability. We show how the results can be applied to control and delayed resonator (DR) problems.
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