Convergence Rate of Quantization Error in Networked Control Systems

In this paper, we investigate the problem of convergence rate of the quantization error in networked control systems. Given bit rate R, we derive the best convergence rate of the quantization error together with a corresponding rate allocation strategy. Specifically, using a min-max eigenvalue problem (MMEP) formulation, it is shown that the error convergence rate is determined by the ratio between |detA| and R where A is the state matrix. It is also shown that the bit rate R can be optimized through a dynamic quantization policy among the unstable modes of the system, such that the convergence rate of the quantization error approaches the optimal solution to the MMEP problem