The finite-time stabilization of discontinuous switched systems is a highly challenging problem. To address this problem, this article proposes a unified controller that achieves fixed-time and preassigned-time stabilization of discontinuous switched systems with time-varying delays, which is superior to finite-time stabilization. Compared with finite-time stabilization results, the settling time for fixed-time stabilization is independent of the initial state of the system. For preassigned-time stabilization, the settling time can be set in advance regardless of the initial state and controller parameters. Also, the fixed-time and preassigned-time stabilization methods proposed in this article are general and can be extended for applications to other nonlinear discontinuous systems with time delays. •A unified control framework is proposed to achieve both fixed-time and preassigned-time stabilization.•Achieve fixed-time stabilization of discontinuous switched systems and obtain more accurate settling times.•Different from finite-time stabilization, the settling time for fixed-time stabilization is independent of the initial state.•The settling time for preassigned-time stabilization can be set ready despite the initial state and controller parameters.