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H∞ Control of Markovian Jump Linear Singularly Perturbed Systems

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Abstract

This paper studies H∞ control of Markovian jump linear singularly perturbed systems (MJLSPSs). A sufficient condition in terms of linear matrix inequalities (LMIs), different from ones in previous existing works, is given for designing H∞ control to overcome the difficulties of solving either Riccati equations or nonlinear matrix inequalities. Then, the jump H∞ controller can be obtained effectively by solving the proposed LMIs. Furthermore, a method is developed for evaluating an allowable upper bound of the singular perturbation parameter, in which a prescribed H∞ performance is satisfied. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed design methods.

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Acknowledgment

This paper is supported by the National Natural Science Foundation of China (61703447), the Key Teachers Research Foundation of the Henan Higher Education Institutions of China (2019GGJS217, 2020GGJS217), the Research Foundation of the Henan Higher Education Institutions of China (21A110027) and the Key Teachers Research Foundation of Zhoukou Normal University.

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  1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China

    Wei Liu & Yanyan Wang

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  1. Wei Liu
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  2. Yanyan Wang
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Correspondence to Wei Liu.

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Liu, W., Wang, Y. H∞ Control of Markovian Jump Linear Singularly Perturbed Systems. Circuits Syst Signal Process 40, 4230–4245 (2021). https://doi.org/10.1007/s00034-021-01676-y

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  • DOI: https://doi.org/10.1007/s00034-021-01676-y

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