This paper considers robust performance analysis and robust H-infinity control for a class of descriptor systems with time-varying and non-linear uncertainties. These uncertainties exist not only in the state, the control input and exogenous input, but also in the derivative of the state. A sufficient condition is firstly proposed to analyse the robust H-infinity performance problem of the unforced systems. Feasible design procedures are presented to construct both the robust state feedback and output feedback controllers such that the closed-loop system has a unique, non-impulsive and asymptotically stable solution and satisfies a robust H-infinity performance criterion. A numerical example is provided to show the efficiency of the approach.