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

Qian Wang (), Xiaojun Zhang (), Yu Shao and Kaibo Shi
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Qian Wang: School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Xiaojun Zhang: School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Yu Shao: School of Automation, Southeast University, Nanjing 210096, China
Kaibo Shi: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China

Mathematics, 2024, vol. 12, issue 19, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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