Quantized stabilization of discrete-time system with input delay

This paper presents the coarsest static quantizer for discrete-time system with delayed-input channel under quadratic stability. With augmentation of the system state and the delayed input, a new system without time delay in the input can be rebuilt. Based on the quadratic stability equivalence of the original system and the rebuilt system, using the isomorphism of the two corresponding admissible control sets that make the systems stabilized, the coarsest quantizer for the system with delay in the control input is derived to be the same as that of the rebuilt system, which is proved to be logarithmic, with the coarsest quantization density characterized by the unstable roots of the open-loop system matrix.