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This paper is concerned with robust passivity analysis of a class of uncertain nonlinear singular time-delay systems as well as with passivity-based sliding mode control of such systems. First we derive a delay-dependent sufficient condition expressed by means of linear matrix inequalities for achieving the generalized quadratic stability and robust passivity of the sliding mode dynamics. Then we show that the system's trajectories can be driven onto the pre-defined switching surface in a finite through synthesis of a sliding mode control law. Finally we present a numerical example that demonstrates the applicability of the derived theoretical results.