Exponential stability of singularly perturbed switched systems with all modes being unstable
In this paper, we study the exponential stability problem for singularly perturbed switched systems(SPSSs), in which subsystems with two-time-scale property are all unstable, and both the destabilizing and stabilizing switching behaviors coexist. To estimate the state divergence during each two cons...
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sg-ntu-dr.10356-1520862021-09-08T01:34:16Z Exponential stability of singularly perturbed switched systems with all modes being unstable Yang, Wu Wang, Yan-Wu Wen, Changyun Daafouz, Jamal School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Singularly Perturbed Switched System Exponential Stability In this paper, we study the exponential stability problem for singularly perturbed switched systems(SPSSs), in which subsystems with two-time-scale property are all unstable, and both the destabilizing and stabilizing switching behaviors coexist. To estimate the state divergence during each two consecutive switching instants, the general property of a two-dimensional matrix involving singular perturbation parameter is explored. The switching sequence is properly reordered to provide an appropriate way to describe different switching behaviors. In addition, multiple composite Lyapunov functions(MCLFs) are employed to derive some stability criteria for the nonlinear SPSSs. Furthermore, by using switching-time-dependent MCLFs and dwell time method, some computable stability condition is given for the linear case. The obtained results show the relationship between the ratio of the stabilizing switching behavior and the singular perturbation parameter. Besides, the obtained results are free of ill-conditioning and stiffness problems. This work is supported by the National Natural Science Foundation of China under Grants 61773172, 61903147, and 51537003, the Natural Science Foundation of Hubei Province of China (2017CFA035), the Fundamental Research Funds for the Central Universities, China (2018KFYYXJJ119) and the Postdoctoral Science Foundation of China under Grant 2019M652644. 2021-09-08T01:34:15Z 2021-09-08T01:34:15Z 2020 Journal Article Yang, W., Wang, Y., Wen, C. & Daafouz, J. (2020). Exponential stability of singularly perturbed switched systems with all modes being unstable. Automatica, 113, 108800-. https://dx.doi.org/10.1016/j.automatica.2019.108800 0005-1098 https://hdl.handle.net/10356/152086 10.1016/j.automatica.2019.108800 2-s2.0-85077311411 113 108800 en Automatica © 2019 Elsevier Ltd. All rights reserved. |
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Engineering::Electrical and electronic engineering Singularly Perturbed Switched System Exponential Stability Yang, Wu Wang, Yan-Wu Wen, Changyun Daafouz, Jamal Exponential stability of singularly perturbed switched systems with all modes being unstable |
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In this paper, we study the exponential stability problem for singularly perturbed switched systems(SPSSs), in which subsystems with two-time-scale property are all unstable, and both the destabilizing and stabilizing switching behaviors coexist. To estimate the state divergence during each two consecutive switching instants, the general property of a two-dimensional matrix involving singular perturbation parameter is explored. The switching sequence is properly reordered to provide an appropriate way to describe different switching behaviors. In addition, multiple composite Lyapunov functions(MCLFs) are employed to derive some stability criteria for the nonlinear SPSSs. Furthermore, by using switching-time-dependent MCLFs and dwell time method, some computable stability condition is given for the linear case. The obtained results show the relationship between the ratio of the stabilizing switching behavior and the singular perturbation parameter. Besides, the obtained results are free of ill-conditioning and stiffness problems. |
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School of Electrical and Electronic Engineering |
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School of Electrical and Electronic Engineering Yang, Wu Wang, Yan-Wu Wen, Changyun Daafouz, Jamal |
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Article |
author |
Yang, Wu Wang, Yan-Wu Wen, Changyun Daafouz, Jamal |
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Yang, Wu |
title |
Exponential stability of singularly perturbed switched systems with all modes being unstable |
title_short |
Exponential stability of singularly perturbed switched systems with all modes being unstable |
title_full |
Exponential stability of singularly perturbed switched systems with all modes being unstable |
title_fullStr |
Exponential stability of singularly perturbed switched systems with all modes being unstable |
title_full_unstemmed |
Exponential stability of singularly perturbed switched systems with all modes being unstable |
title_sort |
exponential stability of singularly perturbed switched systems with all modes being unstable |
publishDate |
2021 |
url |
https://hdl.handle.net/10356/152086 |
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1710686925453524992 |