On the absence of rate loss in decentralized sensor and controller structure for asymptotic stability

We consider a noiseless multi-sensor LTI system where the initial state has a continuous density over a bounded set and the channels connecting the sensors to the controller are discrete and noiseless. We study the rate requirements for the stability of such a system. We show that when the overall system is stabilizable and detectable, the rate required for asymptotic stability is at most an arbitrarily small epsi > 0 larger than Sigma_|lambdai| > 1 log₂(|lambda_i|) where lambda_i´s are the open-loop eigenvalues of the system. Thus, there is no loss in performance due to decentralization. We provide a sequential encoding scheme achieving this rate