Robust passivity analysis of delayed singular systems subject to parametric uncertainties

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.