Stability with Prescribed Convergence Time Applied to Estimation and Control

Abstract

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.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.

Keywords