Decentralized control of the oscillators in large and changing communication networks

The problem of synchronizing the oscillators in a telecommunication network, using local phase-locking loops, is one of decentralized control in a large and unknown system. This contribution investigates the feasibility of designing phase regulators for compensation of disturbances that include oscillator drift, initial phase, and frequency differences between oscillators, and phase shifts originating in the transmission lines ("jitter"). The analysis yields design of a common regulator of PII2-type, which renders all regulated subsets of a given maximum network stable, and hence is able to retain stability even under temporary line failure, shutdown, or startup of arbitrary regulators, or expansion of the network up to a maximum. The network may be either size limited only or arranged in a two-level hierarchy. Stability domains are computed, and examples indicate that application is feasible even for very large networks (up to 1000 nodes).