Optimality of the logarithmic quantizer for stabilization of linear systems: Achieving the minimum data rate

This paper investigates the optimality of the logarithmic quantizer on stabilization of linear systems. It is shown that a finite-level logarithmic quantizer can asymptotically achieve the well-known minimum average data rate for stabilizing an unstable MIMO linear discrete-time system. A time-sharing protocol is proposed to allocate bits to subsystems, each associated with an unstable eigenvalue of the system, and the stability of the system is established using a single logarithmic quantizer and controller.