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Volume 10 Issue 4
Apr.  2023

IEEE/CAA Journal of Automatica Sinica

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F. Tatari and H. Modares, “Deterministic and stochastic fixed-time stability of discrete-time autonomous systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 945–956, Apr. 2023. doi: 10.1109/JAS.2023.123405
Citation: F. Tatari and H. Modares, “Deterministic and stochastic fixed-time stability of discrete-time autonomous systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 945–956, Apr. 2023. doi: 10.1109/JAS.2023.123405

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

doi: 10.1109/JAS.2023.123405
Funds:  This work relates to Department of Navy award N00014-22-1-2159 issued by the Office of Naval Research
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  • 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.

     

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    Highlights

    • The deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems are presented in this paper
    • 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, the sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness is resulted 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 fixedtime attractive systems, and the 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

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