Stability Analysis of Finite-Level Quantized Discrete-Time Linear Control Systems

This paper investigates the stability of discrete-time linear time-invariant systems subject to finite-level logarithmic quantized feedback. Both state feedback and output feedback are considered. A linear matrix inequality (LMI) approach is developed to estimate, for a given controller and a given finite-level quantizer, a set of admissible initial states and an associated attractor set in a neighborhood of the origin such that all state trajectories starting in the first set will converge to the attractor in a finite time and will never leave it. Furthermore, when two such sets are a priori specified, we develop sufficient conditions to design a finite-level logarithmic quantizer for a given stabilizing state or output feedback controller.