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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Main Authors: Jiabao Gu, Hui Wang, Wuquan Li
Format: Article
Language:English
Published: AIMS Press 2022-08-01
Series:Mathematical Biosciences and Engineering
Subjects:
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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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