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Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma.