Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers
This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic...
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AIMS Press
2022-08-01
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Series: | Mathematical Biosciences and Engineering |
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Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022516?viewType=HTML |
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author | Jiabao Gu Hui Wang Wuquan Li |
author_facet | Jiabao Gu Hui Wang Wuquan Li |
author_sort | Jiabao Gu |
collection | DOAJ |
description | This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example. |
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id | doaj.art-1cfc963a1d96488284064cf977ebc2a3 |
institution | Directory Open Access Journal |
issn | 1551-0018 |
language | English |
last_indexed | 2024-04-13T12:57:24Z |
publishDate | 2022-08-01 |
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series | Mathematical Biosciences and Engineering |
spelling | doaj.art-1cfc963a1d96488284064cf977ebc2a32022-12-22T02:46:01ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-08-011911110711108510.3934/mbe.2022516Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powersJiabao Gu0Hui Wang1Wuquan Li2School of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaThis paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example.https://www.aimspress.com/article/doi/10.3934/mbe.2022516?viewType=HTMLstochastic nonlinear systemsmarkovian switchingtime-varying powersoutput-feedbackstabilization |
spellingShingle | Jiabao Gu Hui Wang Wuquan Li Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers Mathematical Biosciences and Engineering stochastic nonlinear systems markovian switching time-varying powers output-feedback stabilization |
title | Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers |
title_full | Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers |
title_fullStr | Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers |
title_full_unstemmed | Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers |
title_short | Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers |
title_sort | output feedback stabilization for stochastic nonlinear systems with markovian switching and time varying powers |
topic | stochastic nonlinear systems markovian switching time-varying powers output-feedback stabilization |
url | https://www.aimspress.com/article/doi/10.3934/mbe.2022516?viewType=HTML |
work_keys_str_mv | AT jiabaogu outputfeedbackstabilizationforstochasticnonlinearsystemswithmarkovianswitchingandtimevaryingpowers AT huiwang outputfeedbackstabilizationforstochasticnonlinearsystemswithmarkovianswitchingandtimevaryingpowers AT wuquanli outputfeedbackstabilizationforstochasticnonlinearsystemswithmarkovianswitchingandtimevaryingpowers |