Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach
In this paper, we study the problem of asymptotic stability of continuous-time positive switched linear systems under both arbitrary and restricted switchings. It is well-known that asymptotic stability under arbitrary switching can be implied by several classes of strong common copositive Lyapunov...
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sg-ntu-dr.10356-1387522020-05-12T07:20:50Z Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach Xu, Yong Dong, Jiu-Gang Lu, Renquan Xie, Lihua School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Switched Systems Positive Systems In this paper, we study the problem of asymptotic stability of continuous-time positive switched linear systems under both arbitrary and restricted switchings. It is well-known that asymptotic stability under arbitrary switching can be implied by several classes of strong common copositive Lyapunov functions (CLFs), i.e., functions whose derivative along the nontrivial system trajectories is negative. However, asymptotically stable positive switched systems may not admit strong common CLFs. The main contribution of this paper is to study the stability problem by requiring only weak common CLFs. Firstly, necessary and sufficient conditions are established for asymptotic stability under arbitrary switching. Among them, an easily verifiable graphical stability criterion, based on the connectivity of the digraphs associated with the subsystem matrices, is proposed. Secondly, we further relax the obtained graphical condition to derive a relaxed weak excitation condition for asymptotic stability under dwell-time switching. Finally, two examples are provided to illustrate the effectiveness of our theoretical results. 2020-05-12T07:20:50Z 2020-05-12T07:20:50Z 2018 Journal Article Xu, Y., Dong, J.-G., Lu, R., & Xie, L. (2018). Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach. Automatica, 97, 278-285. doi:10.1016/j.automatica.2018.04.037 0005-1098 https://hdl.handle.net/10356/138752 10.1016/j.automatica.2018.04.037 2-s2.0-85052325154 97 278 285 en Automatica © 2018 Elsevier Ltd. All rights reserved. |
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Engineering::Electrical and electronic engineering Switched Systems Positive Systems Xu, Yong Dong, Jiu-Gang Lu, Renquan Xie, Lihua Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
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In this paper, we study the problem of asymptotic stability of continuous-time positive switched linear systems under both arbitrary and restricted switchings. It is well-known that asymptotic stability under arbitrary switching can be implied by several classes of strong common copositive Lyapunov functions (CLFs), i.e., functions whose derivative along the nontrivial system trajectories is negative. However, asymptotically stable positive switched systems may not admit strong common CLFs. The main contribution of this paper is to study the stability problem by requiring only weak common CLFs. Firstly, necessary and sufficient conditions are established for asymptotic stability under arbitrary switching. Among them, an easily verifiable graphical stability criterion, based on the connectivity of the digraphs associated with the subsystem matrices, is proposed. Secondly, we further relax the obtained graphical condition to derive a relaxed weak excitation condition for asymptotic stability under dwell-time switching. Finally, two examples are provided to illustrate the effectiveness of our theoretical results. |
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School of Electrical and Electronic Engineering |
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School of Electrical and Electronic Engineering Xu, Yong Dong, Jiu-Gang Lu, Renquan Xie, Lihua |
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Article |
author |
Xu, Yong Dong, Jiu-Gang Lu, Renquan Xie, Lihua |
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Xu, Yong |
title |
Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
title_short |
Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
title_full |
Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
title_fullStr |
Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
title_full_unstemmed |
Stability of continuous-time positive switched linear systems : a weak common copositive Lyapunov functions approach |
title_sort |
stability of continuous-time positive switched linear systems : a weak common copositive lyapunov functions approach |
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2020 |
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https://hdl.handle.net/10356/138752 |
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1681059790608924672 |