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This paper proposes the integration of internal and external clock synchronization by a combination of a fault-tolerant distributed algorithm for clock state correction with a central algorithm for clock rate correction. By means of hardware and simulation experiments it is shown that this combination improves the precision of the global time base in a distributed single cluster system while reducing the need for high-quality oscillators. Simulation results have shown that the rate-correction algorithm contributes not only in the internal clock synchronization of a single cluster system, but it can be used for external clock synchronization of a multi-cluster system with a reference clock. Therefore, deployment of the rate-correction algorithm integrates internal and external clock synchronization in one mechanism. Experimental results show that a failure in the clock rate correction does not hinder the distributed fault-tolerant clock state synchronization algorithm, since the state correction operates independently from the rate correction. The paper introduces new algorithms and presents experimental results on the achieved improvements in the precision measured in a time-triggered system. Results of simulation experiments of the new algorithms in single-cluster and multi-cluster configurations are also presented.