Abstract
This paper is concerned with the mean-square exponential stability problem for a class of impulsive stochastic systems with delayed impulses. The delays exhibit in both continuous subsystem and discrete subsystem. By constructing piecewise time-varying Lyapunov functions and Razumikhin technique, sufficient conditions are derived which guarantee the mean-square exponential stability for impulsive stochastic delay system. It is shown that the obtained stability conditions depend both on the lower bound and the upper bound of impulsive intervals, and the stability of system is robust with regard to sufficiently small impulse input delays. Finally, two examples are proposed to verify the efficiency of the proposed results.
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Recommended by Associate Editor Yingmin Jia under the direction of Editor PooGyeon Park. This work is supported by NNSF of China under grants 61273091, 61104007, 61273123, 61304066, Natural Science Foundation of Shandong province under grant ZR2011FM033, Shandong Provincial Scientific Research Reward Foundation for Excellent Young and Middle-aged Scientists of China under grant BS2011DX013, BS2012SF008, Program for New Century Excellent Talents in University NCET-13-0878, and Taishan Scholar Project of Shandong Province of China.
Dandan Wang received the M.S. degree in Operations Research and Control Theory from Qufu Normal University in 2015. Her research interests include impulsive switched control theory and its application to control of the world.
Lijun Gao received the Ph.D. degree in Operations Research and Control Theory from Qufu Normal University in 2009. Her research interests include switching impulsive control theory, sliding model control, nonholonomic control and its application to control of the world.
Yingying Cai received the B.S. degree in Applied Mathematics from Dezhou University in 2013. Her research interests include impulsive time delay control and finite time stability.
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Wang, D., Gao, L. & Cai, Y. Mean-square exponential stability of impulsive stochastic time-delay systems with delayed impulse effects. Int. J. Control Autom. Syst. 14, 673–680 (2016). https://doi.org/10.1007/s12555-014-0468-7
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DOI: https://doi.org/10.1007/s12555-014-0468-7