Networked control of uncertain systems over data rate limited and lossy channels

This paper studies stabilization of uncertain systems over finite data rate and lossy channels. Limitations on data rate and packet loss probability are derived, characterized by the product of the eigenvalues of the plant. It is worth noting that even if we assume the most conservative plant dynamics, existing limitations for nominal plants are looser than those given in this paper. This fact implies that plant uncertainties cause strictly higher requirements in communication. We consider linear discrete-time systems with parametric uncertainties and employ uniform quantizers, which have the simplest quantization structure. Under the setup, a necessary condition and a sufficient condition for stability are derived. In particular, for scalar plants case, the conditions are exact. They coincide with the existing results for nominal plants as a special case and hence generalize them to the uncertain case.