Stability of Discrete-time Control Systems with Uniform and Logarithmic Quantizers

:This paper deals with stability analysis of discrete-time linear systems involving finite quantizers on the input of the controlled plant. Two kinds of quantization are analyzed: uniform and logarithmic. Through LMI-based conditions, an attractor of the state trajectories and a set of admissible initial conditions are determined. A method is proposed to compare the performances of the two kinds of quantization in terms of the dimensions of the attractor, considering a scenario of Networked Control Systems (NCS). Computational issues are discussed and a numerical example is presented to validate the work.