The use of linear multivariable feedback control to achieve a nonovershooting step response is considered for multi-input multi-output (MIMO) linear time-invariant (LTI) descriptor systems. The use of dynamic output feedback control to improve the transient response to a step input is also considered for MIMO and LTI descriptor systems. We design a state feedback controller and a dynamic output feedback for MIMO and LTI descriptor systems to asymptotically stabilise and track a step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions.