Abstract
This paper is concerned with the problem of \(H_{\infty }\) model reduction for two-dimensional (2-D) discrete Markovian jump systems. The mathematical model of 2-D Markovian jump systems is described by the Fornasini–Marchesini (F–M) second model. Our attention is focused on the design of a 2-D reduced-order model, which ensures the model error system to be stochastically stable and has a prescribed \(H_{\infty }\) performance index. By using the Lyapunov functional approach and introducing some zero equations, a new condition for \(H_{\infty }\) performance analysis of model error system is developed. Based on this condition, the desired reduced-order model parameters can be obtained by solving a set of linear matrix inequalities. Two examples are presented to show the effectiveness of the proposed method.
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The authors would like to thank the editor and anonymous reviewers for their many helpful comments and suggestions to improve the quality of this paper.
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Badie, K., Alfidi, M. & Chalh, Z. \(H_{\infty }\) Model Reduction for 2-D Discrete Markovian Jump Systems. J Control Autom Electr Syst 32, 18–29 (2021). https://doi.org/10.1007/s40313-020-00662-0
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DOI: https://doi.org/10.1007/s40313-020-00662-0