This chapter explores advancements in achieving stability within prescribed convergence time constraints. Drawing from the evolution of stability concepts, including finite-time stability (FTS), fixed-time stability (FxTS), and predefined-time stability (PTS), the chapter presents strategies to address the limitations of traditional FTS methods. Furthermore, it introduces a novel two-stage super-twisting algorithm (STA) that ensures robust prescribed-time state convergence by employing both time-varying and switching gains. By tuning these gains, we guarantee that the proposed algorithm’s analytic solution robustly reaches the origin exactly at the prescribed time. Numerical simulations involving a state-observer-based control problem for a perturbed damped pendulum validate its performance. The results show that the estimation errors converge robustly to the origin at the prescribed instants and remain there afterward. Moreover, a second-order sliding mode is obtained for the controller, driving the tracking errors asymptotically to the origin.