A Fixed-/Preassigned-Time Stabilization Approach for Discontinuous Systems Based on Strictly Intermittent Control

The classical results of fixed-time stabilization (FxTS) are generally achieved via nonintermittent control, as well as cannot be employed to deal with discontinuous systems and strictly intermittent control. In this article, we establish a novel FxTS method for analyzing fixed-time convergence and newly develop a strictly intermittent control scheme to stabilize discontinuous systems within a fixed time based on it. The presented method can also be used to effectively estimate the settling time and to simultaneously reveal how the control period, control width, and control gain affect the convergence time of the controlled system. Additionally, we also extend the proposed FxTS method and use it to design a new strictly intermittent control scheme for achieving the preassigned-time stabilization (PaTS) of discontinuous systems. Finally, an example of Chua's circuit is provided to illustrate the feasibility and applicability of the established FxTS and PaTS methods.