The paper addresses the aspects of stability for real-time systems with varying sampling time, where the sampling time is chosen by a scheduler. To motivate, two examples are given in which instability occurs due to variations in sampling time. Two possible solutions are presented to guarantee stability. In the first method restrictions on the scheduling strategy are opposed, which allow immediate switching fromfast to slow sampling but require to stay for at least a minimum time with slow sampling before switching back to fast sampling again. The second method suggests an optimal controller design in which a bound on the cost, for all possible scheduling strategies, is computed. This results in a piecewise constant state feedback control law and guarantees stability regardless of scheduling.