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This paper considers the problem of stochastic stability and H∞ control for time-delay systems with randomly Markovian jumping parameters. A new approach is proposed to analyze the delay-dependent condition on the stochastic stability by the stochastic Lyapunov-Krasovskii functional approach. It is shown that this new stochastic stability condition combines the so-called delay-independent and delay-dependent conditions. The H∞ disturbance attenuation problem of the systems is also addressed. A numerical example illustrates the effectiveness of the proposed approach, and the conservativeness is compared with existing results.