Robust Stability of Switched Interconnected Systems with Switching Uncertainties
This paper investigates the problem of robust stability for a class of switched interconnected systems characterized by unstable modes, time-varying state delays, and switching uncertainties. Switching uncertainties cause variations in both the nominal switching sequence and the prescribed switching...
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/10/1554 |
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| author | Huanbin Xue Xiaopeng Yang |
| author_facet | Huanbin Xue Xiaopeng Yang |
| author_sort | Huanbin Xue |
| collection | DOAJ |
| description | This paper investigates the problem of robust stability for a class of switched interconnected systems characterized by unstable modes, time-varying state delays, and switching uncertainties. Switching uncertainties cause variations in both the nominal switching sequence and the prescribed switching instants, which significantly impact system stability. To address this, two novel concepts—namely, the generalized nominal switching signal and the composite switching signal—are introduced under switching uncertainty disturbances. Additionally, a new index, termed the generalized mode changing rate, is proposed. Building on these concepts and index, the idea of the vector Lyapunov function and average dwell time method are further incorporated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to demonstrate the effectiveness and validity of the proposed theory. |
| format | Article |
| id | doaj-art-21173f41a9a548a0abd241eec074aebe |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-21173f41a9a548a0abd241eec074aebe2025-08-20T01:56:31ZengMDPI AGMathematics2227-73902025-05-011310155410.3390/math13101554Robust Stability of Switched Interconnected Systems with Switching UncertaintiesHuanbin Xue0Xiaopeng Yang1School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, ChinaThis paper investigates the problem of robust stability for a class of switched interconnected systems characterized by unstable modes, time-varying state delays, and switching uncertainties. Switching uncertainties cause variations in both the nominal switching sequence and the prescribed switching instants, which significantly impact system stability. To address this, two novel concepts—namely, the generalized nominal switching signal and the composite switching signal—are introduced under switching uncertainty disturbances. Additionally, a new index, termed the generalized mode changing rate, is proposed. Building on these concepts and index, the idea of the vector Lyapunov function and average dwell time method are further incorporated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to demonstrate the effectiveness and validity of the proposed theory.https://www.mdpi.com/2227-7390/13/10/1554robust stabilityswitched systemswitching uncertaintiesunstable modestime delay |
| spellingShingle | Huanbin Xue Xiaopeng Yang Robust Stability of Switched Interconnected Systems with Switching Uncertainties Mathematics robust stability switched system switching uncertainties unstable modes time delay |
| title | Robust Stability of Switched Interconnected Systems with Switching Uncertainties |
| title_full | Robust Stability of Switched Interconnected Systems with Switching Uncertainties |
| title_fullStr | Robust Stability of Switched Interconnected Systems with Switching Uncertainties |
| title_full_unstemmed | Robust Stability of Switched Interconnected Systems with Switching Uncertainties |
| title_short | Robust Stability of Switched Interconnected Systems with Switching Uncertainties |
| title_sort | robust stability of switched interconnected systems with switching uncertainties |
| topic | robust stability switched system switching uncertainties unstable modes time delay |
| url | https://www.mdpi.com/2227-7390/13/10/1554 |
| work_keys_str_mv | AT huanbinxue robuststabilityofswitchedinterconnectedsystemswithswitchinguncertainties AT xiaopengyang robuststabilityofswitchedinterconnectedsystemswithswitchinguncertainties |