Data rate limitations for stabilization of uncertain systems over lossy channels

This paper considers data rate limitations for mean square stabilization of uncertain discrete-time linear systems via finite-data-rate and lossy channels. For a plant having parametric uncertainties, a necessary condition and a sufficient condition are derived, represented by the data rate, the packet loss probability, uncertainty bounds on plant parameters, and the unstable eigenvalues of the plant. The results extend those existing in the area of networked control, and in particular, the condition is exact for the scalar plant case.