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Article

Finite-Time Asynchronous H∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems

by
Qian Wang
1,*,
Xiaojun Zhang
1,*,
Yu Shao
2 and
Kaibo Shi
3
1
School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Automation, Southeast University, Nanjing 210096, China
3
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
*
Authors to whom correspondence should be addressed.
Mathematics 2024, 12(19), 3036; https://doi.org/10.3390/math12193036
Submission received: 21 August 2024 / Revised: 18 September 2024 / Accepted: 26 September 2024 / Published: 28 September 2024
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications in Science and Engineering, 3rd Edition)
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Abstract

This article explores the finite-time control problem associated with a specific category of non-homogeneous hidden semi-Markov jump systems. Firstly, a hidden semi-Markov model is designed to characterize the asynchronous interactions that occur between the true system mode and the controller mode, and emission probabilities are used to establish relationships between system models and controller modes. Secondly, a novel piecewise homogeneous method is introduced to tackle the non-homogeneous issue by taking into account the time-dependent transition rates for the jump rules between different modes of the system. Thirdly, an asynchronous controller is developed by applying Lyapunov theory along with criteria for stochastic finite-time boundedness, ensuring the specified H∞ performance level is maintained. Finally, the effectiveness of this method is verified through two simulation examples.
Keywords: non-homogeneous hidden semi-Markov jump systems; stochastic finite-time boundedness; emission probabilities non-homogeneous hidden semi-Markov jump systems; stochastic finite-time boundedness; emission probabilities

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MDPI and ACS Style

Wang, Q.; Zhang, X.; Shao, Y.; Shi, K. Finite-Time Asynchronous H∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems. Mathematics 2024, 12, 3036. https://doi.org/10.3390/math12193036

AMA Style

Wang Q, Zhang X, Shao Y, Shi K. Finite-Time Asynchronous H∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems. Mathematics. 2024; 12(19):3036. https://doi.org/10.3390/math12193036

Chicago/Turabian Style

Wang, Qian, Xiaojun Zhang, Yu Shao, and Kaibo Shi. 2024. "Finite-Time Asynchronous H∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems" Mathematics 12, no. 19: 3036. https://doi.org/10.3390/math12193036

APA Style

Wang, Q., Zhang, X., Shao, Y., & Shi, K. (2024). Finite-Time Asynchronous H∞ Control for Non-Homogeneous Hidden Semi-Markov Jump Systems. Mathematics, 12(19), 3036. https://doi.org/10.3390/math12193036

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