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This study is concerned with the stability and stabilisability problems of networked control systems (NCSs) with partly quantised information. More precisely, the remote state variables transported from other sub-systems experience different network-induced time delays and quantisation errors, whereas the local state variables do not. This consideration is much more natural in NCSs because of the distributive nature of sensors and controllers, even systems. Network-induced time delays are introduced as a Markov chain and quantisation errors are represented as convex polytopic uncertainties. Based on the Lyapunov-Krasovskii functional approach, sufficient conditions for the existence of a quantised robust H∞ output feedback controller for NCSs are presented. Such conditions are obtained in terms of bilinear matrix inequalities (BMIs). Furthermore, a cone complementarity algorithm is utilised to convert these BMIs into a convex optimisation problem. Finally, a simulation example is provided to demonstrate the efficiency of proposed theorems.