Halanay-type inequality with delayed impulses and its applications


In this study, some properties of a novel Halanay-type inequality that simultaneously contains impulses and delayed impulses are investigated. Two concepts with respect to average impulsive gain are proposed to describe hybrid impulsive strength and hybrid delayed impulsive strength. Then, using the obtained results, two stability criteria are derived for the linear systems with impulses and delayed impulses. It is found that the stability of impulsive systems is robust with respect to delayed impulses of which the magnitude strength is relatively small. Whereas, if the impulse strength is small, the time-delayed impulses can also promote the stability of unstable systems. Two numerical examples are employed to illustrate the efficiency of our results.

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This work was supported by National Natural Science Foundation of China (Grant No. 61573102), Natural Science Foundation of Jiangsu Province (Grant No. BK20170019), Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002), and Graduate Research and Innovation Program of Jiangsu Province (Grant No. KYCX18_0052).

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Correspondence to Jianquan Lu.

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Wang, Y., Lu, J. & Lou, Y. Halanay-type inequality with delayed impulses and its applications. Sci. China Inf. Sci. 62, 192206 (2019). https://doi.org/10.1007/s11432-018-9809-y

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  • Halanay-type inequality
  • hybrid impulses
  • average impulsive gain
  • delayed impulses
  • linear impulsive systems