Abstract
This paper is concerned with the detectability of discrete-time mean-field linear systems with periodic coefficients and multiplicative noise. By use of \(\mathcal {H}\)-representation method and orthogonal decomposition, a monodromy operator is constructed for the considered systems. According to the spectrum of monodromy operator, a Popov-Belevitch-Hautus (PBH) criterion is proven for detectabilty of the considered systems. Furthermore, by applying the obtained PBH criterion, an extended Lyapunov stability theorem is shown to establish the relationship between detectability and asymptotic mean square stability.
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Acknowledgement
This work was supported by the Natural Science Foundation of Shandong Province (ZR2016FM16), the SDUST Research Fund (No. 2015TDJH105), and Elite Project of Shandong University of Science and Technology.
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Ma, H. (2022). Detectability of Discrete-Time Mean-Field Linear Stochastic Systems with Periodic Coefficients. In: Jia, Y., Zhang, W., Fu, Y., Yu, Z., Zheng, S. (eds) Proceedings of 2021 Chinese Intelligent Systems Conference. Lecture Notes in Electrical Engineering, vol 805. Springer, Singapore. https://doi.org/10.1007/978-981-16-6320-8_4
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DOI: https://doi.org/10.1007/978-981-16-6320-8_4
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