Multivariable quadratically-stabilizing quantizers with finite density

This paper deals with quadratic stabilization of discrete-time multiple-input (MI) systems by means of quantized static feedback. We consider the minimization of quantization density, which is still an open problem for MI systems. Our first contribution in this regard is to partially derive the structure that a quantizer that minimizes density for an MI system should have. The second and main contribution of the paper is to develop a systematic design procedure for finite-density quadratically-stabilizing quantizers for MI systems. The resulting quantizers have a simple geometric structure and can be implemented via simple function evaluations. To the best of the authors' knowledge, no such design of finite-density quadratically-stabilizing quantizers has been previously proposed in the literature for general MI systems.