Communication constraints for decentralized stabilizability with time-invariant policies

In this note, we study communication requirements for decentralized control schemes when sensors and controllers are connected via noiseless digital channels and system noises are bounded. Under various information structures, and within the class of time-invariant encoding and control policies, we quantify achievable rates, and obtain fixed-rate and delayless encoders and decoders that achieve boundedness in the state estimation errors at the controllers. We use distributed coding theoretic approaches to show that when the sensors do not collaborate, it is sufficient for the controllers to share information amongst themselves but not with the sensors. Sensor collaboration, however, leads to improvement in rate performance.