Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

• Published in: IEEE/CAA journal of automatica sinica Vol. 10; no. 4; pp. 945 - 956
• Main Authors: Tatari, Farzaneh, Modares, Hamidreza
• Format: Journal Article
• Language: English
• Published: Piscataway Chinese Association of Automation (CAA) 01.04.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Mechanical Engineering Department,Michigan State University,Michigan 48824-1226 USA
• Subjects: Autonomous systems; Discrete time systems; Discrete-time (DT) systems; fixed-time stability; nonlinear systems; Perturbation; Perturbation methods; Sensitivity; Settling; Simulation; Stability; Stability analysis; stochastic systems; Time functions; Upper bound; Upper bounds; stochastic systems; Discrete-time (DT) systems; non-linear systems; fixed-time stability
• ISSN: 2329-9266; 2329-9274
• DOI: 10.1109/JAS.2023.123405

This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified. Extensions to systems under deterministic perturbations as well as stochastic noise are then considered. For the former, sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions. For the latter, sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented. The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems, and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems. Illustrative examples are given along with simulation results to verify the introduced results.