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H∞ Filtering for Markovian Jump Linear Systems with Uncertain Transition Probabilities

  • Control Theory and Applications
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Abstract

This paper studies the H∞ filtering problem of stochastic linear systems subject to Markovian jump and multiplicative noise. The transition probabilities are considered to be uncertain. A unified form of filters is constructed for both continuous-time and discrete-time stochastic systems. With the new decoupling technique for the coupling terms between Lyapunov matrices and filtering parameters, sufficient conditions of stochastic stability and H∞ performance of filtering error system are derived. Based on these conditions, the filter is designed with less coupling matrices and the filter gain matrices are obtained by calculating a set of linear matrix inequalities. Finally, three examples are presented to test the effectiveness of the obtained method.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Xi-Kui Liu & Ji-Jing Zhuang

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Yan Li

Authors
  1. Xi-Kui Liu
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  2. Ji-Jing Zhuang
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  3. Yan Li
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Corresponding author

Correspondence to Yan Li.

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Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This work was supported by National Natural Science Foundation of China under Grant 61972236 and Shandong Provincial Natural Science Foundation under Grant ZR2018MF013.

Xikui Liu received his M.S. degree from Shandong University of Science and Technology, and a Ph.D. degree from Huazhong University of Science and Technology, China, in 2000 and 2004, respectively. He is a Professor of Shandong University of Science and Technology, China. His interests include multi-objective optimization, graph theory, linear and nonlinear stochastic optimal control.

JiJing Zhuang received her B.E. degree from the Xingtan College, Qufu Normal University, Jinan, China, in 2017, where she is currently pursuing a Ph.D. degree with the Shandong University of Science and Technology, Qingdao, China. Her research interests include linear and nonlinear stochastic systems robust H∞ filtering.

Yan Li received her M.S. and Ph.D. degrees from Shandong University of Science and Technology, China, in 2006 and 2015, respectively. She is an Associate Professor of Shandong University of Science and Technology, China. Her research interests include linear and nonlinear stochastic control, mean-field systems, robust H∞ control, stochastic stability and stabilization, and fuzzy adaptive control.

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Liu, XK., Zhuang, JJ. & Li, Y. H∞ Filtering for Markovian Jump Linear Systems with Uncertain Transition Probabilities. Int. J. Control Autom. Syst. 19, 2500–2510 (2021). https://doi.org/10.1007/s12555-020-0129-y

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  • DOI: https://doi.org/10.1007/s12555-020-0129-y

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