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Journal of Control Science and Engineering
Volume 2016, Article ID 9527680, 8 pages
Research Article

Some New Generalized Retarded Gronwall-Like Inequalities and Their Applications in Nonlinear Systems

1School of Mathematics, Qilu Normal University, Jinan, Shandong 250013, China
2Department of Automation, China University of Petroleum (Beijing), Changping, Beijing 102249, China

Received 15 November 2015; Accepted 15 February 2016

Academic Editor: Petko Petkov

Copyright © 2016 Haiyong Qin 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.


The Gronwall inequalities are of significance in mathematics and engineering. This paper generalizes the Gronwall-like inequalities from different perspectives. Using the proposed inequalities, the difficulties to discuss the controllability of integrodifferential systems of mixed type can be solved. Meanwhile, two examples as their applications are also given to show the effectiveness of our main results.