Minimum Data Rate for Mean Square Stabilization of Discrete LTI Systems Over Lossy Channels

This note investigates the minimum data rate for mean square stabilization of discrete linear time-invariant systems over a lossy channel. The packet dropout process of the channel is modeled as an independent and identically distributed process. For general single input systems, the minimum data rate is explicitly given in terms of unstable eigenvalues of the open loop matrix and the packet dropout rate, which clearly reveals the amount of the additional bit rate required to counter the effect of packet dropouts on stabilization. Sufficient data rate conditions for the mean square stabilization of multiple input systems are derived as well.