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Volume 2018, Article ID 8701219, 8 pages
Research Article

Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Peng Li,1 Xiaodi Li,1,2 and Jinde Cao1,3

1School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2Institute of Data Science and Technology and Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, Shandong Normal University, Jinan 250014, China
3School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210 096, China

Correspondence should be addressed to Xiaodi Li; nc.ude.unds@dxl

Received 30 July 2017; Revised 24 November 2017; Accepted 28 December 2017; Published 24 January 2018

Academic Editor: Peter Galambos

Copyright © 2018 Peng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.