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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Main Authors: Yang, Wu, Wang, Yan-Wu, Wen, Changyun, Daafouz, Jamal
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2021
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Online Access:https://hdl.handle.net/10356/152086
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Institution: Nanyang Technological University
Language: English
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spelling 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.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Singularly Perturbed Switched System
Exponential Stability
spellingShingle 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
description 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.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Yang, Wu
Wang, Yan-Wu
Wen, Changyun
Daafouz, Jamal
format Article
author Yang, Wu
Wang, Yan-Wu
Wen, Changyun
Daafouz, Jamal
author_sort 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
_version_ 1710686925453524992