Stability analysis of input and output finite level quantized discrete-time linear control systems

This paper analyzes the stability of input and output quantized discrete-time linear control systems considering static finite-level logarithmic quantizers. The sector bound approach together with a relaxed stability notion are applied to derive LMI based conditions for estimating a set of initial conditions and its attractor assuming that the controller and quantizers are known a priori. These conditions ensure that all state trajectories belonging to the first set will enter the attractor in a finite time and remains inside it. A numerical example is presented to illustrate the application of the derived results.