Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers

Jiabao Gu; Hui Wang; Wuquan Li; Jiabao Gu; Hui Wang; Wuquan Li

doi:10.3934/mbe.2022516

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11071-11085. doi: 10.3934/mbe.2022516

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Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers

School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

Received: 05 July 2022 Revised: 23 July 2022 Accepted: 27 July 2022 Published: 03 August 2022

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.
- stochastic nonlinear systems,
- Markovian switching,
- time-varying powers,
- output-feedback,
- stabilization
Citation: Jiabao Gu, Hui Wang, Wuquan Li. Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11071-11085. doi: 10.3934/mbe.2022516

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Abstract

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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