Towards a Packet-based Control Theory - Part II: Rate Issues

Following our first paper of stabilizing a linear time invariant (LTI) system in a packet-based network, which appeared in ACC 05, this paper further studies various rate issues associated with networked control systems. Specifically, networks with finite bandwidth and packet drops and systems with finite control inputs are studied in detail. Similar to what we did in the previous paper, we assume that the state information is transmitted to the controller over a packet-based network. We also assume that there is a perfect link from the controller to the plant. However, we change the notion of the system being asymptotically stable to almost sure stable which is in a probabilistic framework. This is because packet drops by the network introduce unavoidable randomness. With the notion of almost sure stability, various rate results under different settings are given. Examples and simulations are provided to demonstrate the results