Abstract
This paper is concerned with the finite-time stability of linear discrete-time stochastic system with time-varying delays and its applications to the consensus problem of multi-agent system. A novel finite-time stability criterion is presented to guarantee that the state of the system does not exceed a prescribed bound during a fixed time interval using the piecewise-like delay method. Then, a corollary is derived for the case without stochastic perturbations. Numerical examples are provided to show the less conservatism and effectiveness of the proposed linear matrix inequality conditions. Finally, the stability results are directly applied to develop the finite-time consensus conditions for the linear multi-agent system with time-varying communication delays. An illustrative example is given to validate the effectiveness of the theoretical results.
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Acknowledgments
This work was supported by the Fundamental Research Funds for the Central Universities (JUSRP51317B, JUSRP211A21), and the National Natural Science Foundation of China under Grant 61272530, 11202084 and 11072059, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012741, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grants 20110092110017 and 20130092110017.
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Appendices
Appendices
1.1 Appendix 1: The notations for the conditions in Theorem 1
1.2 Appendix 2: The bounded estimation of \(V(0)\)
with
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Hu, M., Cao, J., Hu, A. et al. A Novel Finite-Time Stability Criterion for Linear Discrete-Time Stochastic System with Applications to Consensus of Multi-Agent System. Circuits Syst Signal Process 34, 41–59 (2015). https://doi.org/10.1007/s00034-014-9838-x
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DOI: https://doi.org/10.1007/s00034-014-9838-x