In this paper, the design of a switched non-PDC controller, for a class of switched nonlinear systems subject to external disturbances is investigated for the purpose of satisfying robust H∞ output-feedback tracking performances. Based on multiple switched non quadratic-like Lyapunov functions, sufficient conditions for the existence of a switched non-PDC controller are formulated in terms of Linear Matrix Inequality (LMI). The efficiency of the proposed approach is illustrated by a numerical example.