Fixed-time Stability of Discrete-time Autonomous Systems

Abstract

The fixed-time stability of autonomous nonlinear discrete-time (DT) systems is studied in this paper. Novel Lyapunov conditions are presented under which the fixed-time stability of autonomous DT system is certified. Extension to systems under perturbations is also considered. The sensitivity to perturbations for fixed-time stable DT systems is analyzed and it is shown that fixed-time attractiveness can be resulted from the presented Lyapunov conditions. The fixed upper bound of the settling-time functions is derived for fixed-time stable and fixed-time attractive systems. An illustrative example with simulations are also given to verify the introduced results.