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In this paper, multiple Lyapunov functions and Lyapunov inequalities are used to investigate the stability of discrete-time switched linear singular (DSLS) systems. Based on the existing criteria of stability for discrete-time switched systems, a sufficient condition of stability of DSLS for arbitrary switching laws is proposed in terms of a set of coupled strict linear inequalities. Then a method to construct a class of multiple Lyapunov functions is presented. Finally, an example is given to illustrate the main results in this paper.