In this paper, the robust non-fragile stabilisation and H control problem is investigated for a class of uncertain discrete-time stochastic systems with Markovian jumping parameters and time-varying delay. The parameter uncertainties are supposed to be time-varying as well as norm-bounded. The aim of the robust non-fragile stabilisation problem is to design a non-fragile state feedback controller which guarantees the robust stability of the closed-loop system for all admissible uncertainties. At the same time, in addition to the robust stability requirement, a prescribed H performance level is required to be achieved for the robust H control problem. By Lyapunov stability theory, delay-segment-dependent conditions for the solvability of these problems are formulated in terms of linear matrix inequality technique. Finally, numerical examples are shown to demonstrate the usefulness and applicability of the proposed design method.