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This paper is concerned with the problem of robust H∞ control for polytopic uncertain discrete-time Markovian jump linear systems over communication networks. The network-induced delay is considered to be time-varying and bounded. A delay-dependent condition is proposed for the design of a mode-independent H∞ controller which ensures robust stochastic stability and a prescribed H∞ performance level for the resulting closed-loop system. An solution of the problem can be obtained by solving a set of linear matrix inequalities(LMIs) that is numerically feasible with commercially available software. A simulation example is provided to demonstrate the effectiveness of the proposed method.