Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems
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 w...
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| Published in | IEEE/CAA journal of automatica sinica Vol. 10; no. 4; pp. 945 - 956 |
|---|---|
| Main Authors | , |
| 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 | |
| Online Access | Get full text |
| ISSN | 2329-9266 2329-9274 |
| DOI | 10.1109/JAS.2023.123405 |
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| Abstract | 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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| AbstractList | This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) sys-tems. 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 pre-sented 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 func-tion fixed upper bound is derived for stochastic DT systems. Illus-trative examples are given along with simulation results to verify the introduced results. 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. |
| Author | Modares, Hamidreza Tatari, Farzaneh |
| AuthorAffiliation | Mechanical Engineering Department,Michigan State University,Michigan 48824-1226 USA |
| AuthorAffiliation_xml | – name: Mechanical Engineering Department,Michigan State University,Michigan 48824-1226 USA |
| Author_xml | – sequence: 1 givenname: Farzaneh surname: Tatari fullname: Tatari, Farzaneh email: tatarifa@msu.edu organization: Michigan State University,Mechanical Engineering Department,Michigan,USA,48824-1226 – sequence: 2 givenname: Hamidreza surname: Modares fullname: Modares, Hamidreza email: modaresh@msu.edu organization: Michigan State University,Mechanical Engineering Department,Michigan,USA,48824-1226 |
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| Keywords | stochastic systems Discrete-time (DT) systems non-linear systems fixed-time stability |
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| Snippet | This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first... This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) sys-tems. Lyapunov conditions are first... |
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| SubjectTerms | 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 |
| Title | Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems |
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