Hyungbo Shim / Daniel Liberzon Stability of linear systems with slow and fast time variation and switching: General case Journal Article In: Nonlinear Analysis: Hybrid Systems, vol. 58, pp. 101626, 2025, ISSN: 1751-570X. @article{nokey,
title = {Stability of linear systems with slow and fast time variation and switching: General case},
author = {Hyungbo Shim and Daniel Liberzon},
doi = {10.1016/j.nahs.2025.101626},
issn = {1751-570X},
year = {2025},
date = {2025-11-01},
urldate = {2025-11-01},
journal = {Nonlinear Analysis: Hybrid Systems},
volume = {58},
pages = {101626},
abstract = {This paper studies exponential stability of linear systems with slow and fast time variation and switching. We use averaging to eliminate the fast dynamics and only retain the slow dynamics. We then use a recent stability criterion for slowly time-varying and switched systems, combined with perturbation analysis, to prove stability of the original system. The analysis involves working with an impulsive system in new coordinates, which enables us to treat a more general class of systems compared to previous work.},
keywords = {Averaging Theory, Nonlinear system, Switched systems},
pubstate = {published},
tppubtype = {article}
}
This paper studies exponential stability of linear systems with slow and fast time variation and switching. We use averaging to eliminate the fast dynamics and only retain the slow dynamics. We then use a recent stability criterion for slowly time-varying and switched systems, combined with perturbation analysis, to prove stability of the original system. The analysis involves working with an impulsive system in new coordinates, which enables us to treat a more general class of systems compared to previous work. |
Sihyun Ahn / Hyungbo Shim / Daniel Liberzon Semi-global practical stability of nonlinear systems with slow and fast time variation and switching in a separable form Proceedings Article In: 2024 IFAC Conference on Analysis and Control of Nonlinear Dynamics and Chaos, 2024. @inproceedings{nokey,
title = {Semi-global practical stability of nonlinear systems with slow and fast time variation and switching in a separable form},
author = {Sihyun Ahn and Hyungbo Shim and Daniel Liberzon},
year = {2024},
date = {2024-06-06},
booktitle = {2024 IFAC Conference on Analysis and Control of Nonlinear Dynamics and Chaos},
abstract = {This paper investigates stability of nonlinear systems, which has the separable form, with time-varying parameters. When the parameters are frozen, the system is stable, and the stability question is for the case when the parameters are fast-varying but its (time-varying) average (defined in a certain sense) varies slowly. Here, we allow the slowly-varying average to be discontinuous as long as its total variation has small growth. While existing results are based on the assumption that the equilibrium is invariant with respect to the parameters, we extend them to the case where the equilibrium is invariant with respect to the average of the fast-varying parameters.},
keywords = {Lyapunov method, Switched systems},
pubstate = {published},
tppubtype = {inproceedings}
}
This paper investigates stability of nonlinear systems, which has the separable form, with time-varying parameters. When the parameters are frozen, the system is stable, and the stability question is for the case when the parameters are fast-varying but its (time-varying) average (defined in a certain sense) varies slowly. Here, we allow the slowly-varying average to be discontinuous as long as its total variation has small growth. While existing results are based on the assumption that the equilibrium is invariant with respect to the parameters, we extend them to the case where the equilibrium is invariant with respect to the average of the fast-varying parameters. |
Hyungbo Shim / Daniel Liberzon Stability of linear systems with slow and fast time variation and switching Proceedings Article In: Proc. of 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 674-678, IEEE, Cancun, Mexico, 2022, ISBN: 978-1-6654-3659-5. @inproceedings{none,
title = {Stability of linear systems with slow and fast time variation and switching},
author = {Hyungbo Shim and Daniel Liberzon},
url = {https://ieeexplore.ieee.org/document/9992853},
doi = {10.1109/CDC51059.2022.9992853},
isbn = {978-1-6654-3659-5},
year = {2022},
date = {2022-12-06},
urldate = {2022-12-06},
booktitle = {Proc. of 2022 IEEE 61st Conference on Decision and Control (CDC)},
pages = {674-678},
publisher = {IEEE},
address = {Cancun, Mexico},
abstract = {We establish exponential stability for a class of linear systems with slow and fast time variation and switching. We use the averaging method to approximate the original system by the average system which only exhibits slow time variation and switching. We then apply a stability criterion recently developed for such systems to prove stability of the average system and, consequently, of the original system.
},
keywords = {Stability of linear systems, Switched systems, Time-varying systems},
pubstate = {published},
tppubtype = {inproceedings}
}
We establish exponential stability for a class of linear systems with slow and fast time variation and switching. We use the averaging method to approximate the original system by the average system which only exhibits slow time variation and switching. We then apply a stability criterion recently developed for such systems to prove stability of the average system and, consequently, of the original system.
|