This study presents a new method for analysis and synthesis of discrete-time linear systems with control input quantisation (a class of logarithmic quantisers is referred as the basis of the study) over a digital network. Looking at the relevant problems from different facet, referring to the sector bound approach and converting quantised control into robust control with sector bounds uncertainties, the study establishes a robust model predictive control strategy to provide a novel and efficient solution to the quantised control issues. Analytically, the study derives the coarsest quantisation density under a certain control performance and the stabilisation conditions for the discrete-time linear systems. Initially as bench tests, two illustrative examples are provided to demonstrate the effectiveness of the proposed procedure and the guideline for potential users.