Stabilization of networked control systems with finite data rate

Networked control system (NCS) is a newly emerging topic within control theory community. In this paper we pay particular attention to the problem concerning data rate constraint. Motivated by many successful results in related research, we study the lowest data rate needed to stabilize an LTI system when the controller structure is limited to be a static state feedback and the channel is modeled as a finite logarithmic quantizer. We prove that the lowest data rate is a function of the system Mahler measure alone. We also give the optimal state feedback controller achieving the lowest data rate and the associated Lyapunov function when proving the closed-loop stability.