Stability analysis of finite-level quantized linear control systems

In this paper we investigate the stability of discrete-time linear time-invariant systems subject to finite-level logarithmic quantized feedback. Both state feedback and output feedback are considered. We develop an LMI approach 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 these two such sets are a priori specified, we develop sufficient conditions for designing a suitable state or output feedback controller, along with a finite-level logarithmic quantizer.