Finite-time and fixed-time stability for nonlinear systems via aperiodically intermittent control

In this paper, we consider the finite-time stability (FIS) and fixed-time stability (FXS) problems for nonlinear systems by employing aperiodically intermittent control. Through the application of an iterative method, several general Lyapunov theorems, along with settling-time estimates of FIS and FXS, are established for aperiodically intermittent controlled nonlinear systems. Furthermore, aperiodically intermittent FIS and FXS control strategies are designed based on our theoretical findings. Additionally, when the uncontrolled time period approaches zero, the aperiodically intermittent controlled system transitions to a continuously controlled nonlinear system. Our results not only extend classical FIS and FXS findings for continuous controlled nonlinear systems but also generalize and enhance existing FIS and FXS results for aperiodically intermittent controlled nonlinear systems. The effectiveness of the proposed method is demonstrated through numerical examples.