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This paper describes the problem of model orderreduction for a class of hybrid discrete-time switched linear systems composed of linear discrete-time invariant subsystems with a switching rule. The paper investigates a novel method to model reduction. The approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure. The error limit depends on the truncated singular values and balanced truncation procedure helps to keep the biggest singular values of the system. A numerical example shows the effectiveness of the proposed approach.