A separation theorem for periodic sharing information patterns in decentralized control

Optimal decentralized control of a discrete-time stochastic system is considered under a periodic sharing information pattern. In this scenario, controllers share information with one-step delay every K time steps. The periodic sharing pattern is a generalization of the previously studied one-step delay sharing pattern, which is known to possess a nonclassical separation property. It is proven that the periodic sharing pattern has an analogous separation property