# American Institute of Mathematical Sciences

## Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks

 a. Department of Mathematics Hunan First Normal University, Changsha, Hunan 410205, China b. School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China c. ool of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China c Jiangsu Provincial Key Laboratory of Networked Collective Intelligence Southeast University, Nanjing, Jiangsu 210096, China d. Department of Information Technology, Hunan Women's University Changsha, Hunan 410002, China e. School of Mathematics and Statistics, Changsha University of Science and Technology Changsha, Hunan 410114, China

* Corresponding author: Jinde Cao

Received  December 2019 Revised  March 2020 Published  June 2020

Fund Project: This work was supported in part by NSF of China(No.11601143, 61833005), Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (No.BM2017002), China Postdoctoral Science Foundation (No.2018M632207) and Teaching Reform Project of Ordinary Colleges and Universities in Hunan Province (No. 844)

In this article, we present several results on Finite-Time Stability (FTS) of impulsive differential inclusion. In order to investigate the FTS problem, a new concept of Finite-Time Stable Function Pair (FTSFP) is proposed. By virtue of average impulsive interval and FTSFP, two unified criteria on FTS of impulsive differential inclusion are obtained, which are effective for both the destabilizing impulses and the stabilizing impulses. In addition, the settling-time depends not only on the initial value, but also on the information of impulsive sequence. As an extension, a delay-independent FTS result of impulsive delayed differential inclusion is presented. Finally, the obtained results are applied to study the FTS of discontinuous impulsive neural networks.

Citation: Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020200
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##### References:
The state trajectories of $x_{i}(t)$ $(i = 1,2)$ without impulsive effects in Example 1
The trajectories of states $x_{i}(t)$ $(i = 1,2)$ with different impulsive sequences in Example 1
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