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Motivated by switched service systems with multiple buffers controlled by a single server to educe multiple output flows simultaneously, the paper introduces a special class of linear hybrid automata. It is proved that the linear hybrid automata can be reduced to a linear discrete-time system with periodic coefficients. Moreover it is shown that the linear hybrid automata admits a periodic trajectory, and the theorem for asymptotic stability of the periodic trajectory are given. Finally, our result is applied to prove stability of the switched server system.