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Limiting Behavior of Hybrid Time-Varying Systems.

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Title: Limiting Behavior of Hybrid Time-Varying Systems.
Authors: Lee, Ti-Chung1 tclee@mail.ee.nsys.edu.tw, Tan, Ying2 yingt@unimelb.edu.au, Mareels, Iven3 imareels@au1.ibm.com
Source: IEEE Transactions on Automatic Control. Nov2022, Vol. 67 Issue 11, p5777-5792. 16p.
Subjects: Time-varying systems, Hybrid systems, Global asymptotic stability, Dynamical systems, Lyapunov functions, Nonlinear systems
Abstract: Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this article, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii–LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Automatic Control is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Lee%2C+Ti-Chung%22">Lee, Ti-Chung</searchLink><relatesTo>1</relatesTo><i> tclee@mail.ee.nsys.edu.tw</i><br /><searchLink fieldCode="AR" term="%22Tan%2C+Ying%22">Tan, Ying</searchLink><relatesTo>2</relatesTo><i> yingt@unimelb.edu.au</i><br /><searchLink fieldCode="AR" term="%22Mareels%2C+Iven%22">Mareels, Iven</searchLink><relatesTo>3</relatesTo><i> imareels@au1.ibm.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Automatic+Control%22">IEEE Transactions on Automatic Control</searchLink>. Nov2022, Vol. 67 Issue 11, p5777-5792. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Time-varying+systems%22">Time-varying systems</searchLink><br /><searchLink fieldCode="DE" term="%22Hybrid+systems%22">Hybrid systems</searchLink><br /><searchLink fieldCode="DE" term="%22Global+asymptotic+stability%22">Global asymptotic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink>
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  Data: Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this article, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii–LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of IEEE Transactions on Automatic Control is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1109/TAC.2021.3122376
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        Text: English
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      – SubjectFull: Time-varying systems
        Type: general
      – SubjectFull: Hybrid systems
        Type: general
      – SubjectFull: Global asymptotic stability
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      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Lyapunov functions
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      – SubjectFull: Nonlinear systems
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              Text: Nov2022
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