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This paper concerns dynamic output feedback design of discrete-time linear switched systems using switched Lyapunov functions (SLF). A new characterization of stability HÂ¿ performance for the switched system under arbitrary switching is first given. The various conditions are given through a family of LMI (linear matrix inequalities) parameterized by a scalar variable which offers an additional degree of freedom, enabling, at the expense of a relatively small degree of complexity in the numerical treatment (one line search), to provide better results compared to previous results. The control is defined as a switched dynamic output feedback which guarantees stability and HÂ¿ performance for the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed conditions.