Further study on stability analysis for Markov linear parameter-varying systems

Likui Wang; Hak-Keung Lam

doi:10.1109/TAC.2025.3580046

Further study on stability analysis for Markov linear parameter-varying systems

Likui Wang
, Hak-Keung Lam

Nanchang Hangkong University
Hebei University of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

45 Downloads (Pure)

Abstract

This article addresses the problem of stability analysis for a class of Markov jump systems with time-varying parameters. Unlike previous studies that assumed a bounded rate of parameter variation, this research allows for an arbitrary parameter variation rate. In addition, a new parameter-dependent homogeneous polynomial Lyapunov function is designed, which depends on both the Markov process and time-varying parameters simultaneously. The switching approach is employed to deal with the derivatives of time-varying parameters, while the average dwell time approach is utilized to handle the switching signal. Thus, a less conservative stability criterion is obtained to ensure the exponentially mean-square stability of the system. Three examples are provided to verify the effectiveness of the obtained results.

Original language	English
Pages (from-to)	7704-7710
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	70
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2025.3580046
Publication status	Published - 31 May 2025

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abstract = "This article addresses the problem of stability analysis for a class of Markov jump systems with time-varying parameters. Unlike previous studies that assumed a bounded rate of parameter variation, this research allows for an arbitrary parameter variation rate. In addition, a new parameter-dependent homogeneous polynomial Lyapunov function is designed, which depends on both the Markov process and time-varying parameters simultaneously. The switching approach is employed to deal with the derivatives of time-varying parameters, while the average dwell time approach is utilized to handle the switching signal. Thus, a less conservative stability criterion is obtained to ensure the exponentially mean-square stability of the system. Three examples are provided to verify the effectiveness of the obtained results.",

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AB - This article addresses the problem of stability analysis for a class of Markov jump systems with time-varying parameters. Unlike previous studies that assumed a bounded rate of parameter variation, this research allows for an arbitrary parameter variation rate. In addition, a new parameter-dependent homogeneous polynomial Lyapunov function is designed, which depends on both the Markov process and time-varying parameters simultaneously. The switching approach is employed to deal with the derivatives of time-varying parameters, while the average dwell time approach is utilized to handle the switching signal. Thus, a less conservative stability criterion is obtained to ensure the exponentially mean-square stability of the system. Three examples are provided to verify the effectiveness of the obtained results.

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JF - IEEE Transactions on Automatic Control

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Further study on stability analysis for Markov linear parameter-varying systems

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