Stabilization of uncertain systems in the presence of finite data-rate feedback

In this paper, we address the stabilizability of uncertain systems in the presence of finite data-rate feedback. In our formulation, a finite data-rate link is used to transmit state measurements between the plant and the controller. We determine sufficient conditions for internal and external stabilizability of the feedback loop. Stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that larger uncertainty can be tolerated at the expense of higher transmission rates. A comparison is established between the sufficient conditions for robust stabilizability and the necessary conditions for the stability of the nominal model. We also suggest how our results can be used to determine the stabilizability of a class of non-linear systems.