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This study deals with the problem of H infin output-feedback control for switched linear discrete-time systems with time-varying delay. A delay-dependent stability criterion for a given H infin performance is derived by employing finite sum equality based on quadratic terms, a new method of estimating the upper bound on the finite sum. Both static and dynamic H infin output-feedback controllers are designed based on a performance analysis. Moreover, a modified cone complementary linearisation algorithm is exploited to solve the non-convex feasibility problem. Numerical examples are given to illustrate the theoretical results.