Abstract
This paper is devoted to stability analysis of discrete-time linear systems with Borel-measurable Markov jump parameters and independent multiplicative noises. The relationships are investigated among several stability concepts about the considered dynamics. Specifically, it is shown that strong exponential stability in the mean square sense can guarantee exponential stability, \(l_2\) input-output stability and stochastic stability to hold. Moreover, both exponential stability and \(l_2\) input-output stability give rise to stochastic stability. By a numerical example, it is demonstrated that Borel-measurable Markov jump systems must not be exponentially stable even if it is stochastically stable.
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Acknowledgment
This work was supported by the Natural Science Foundation of Shandong Province (ZR2016FM16), the Natural Science Foundation of China (No. 61673013), the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2016RCJJ031) and SDUST Research Fund (No. 2015TDJH105).
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Ma, H., Cui, Y., Wang, Y. (2020). Stability Analysis of Discrete-Time Stochastic Systems with Borel-Measurable Markov Jumps. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2019 Chinese Intelligent Systems Conference. CISC 2019. Lecture Notes in Electrical Engineering, vol 594. Springer, Singapore. https://doi.org/10.1007/978-981-32-9698-5_2
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DOI: https://doi.org/10.1007/978-981-32-9698-5_2
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