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A generalized Halanay inequality on impulsive delayed dynamical systems and its applications |
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| Authors: | Quanjun Wu Hua Zhang Lan XiangJin Zhou |
| Affiliation: | a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China c School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China d Department of Mathematics and Computer Science, Tongren College, Tongren 554300, China e Department of Physics, School of Science, Shanghai University, Shanghai 200444, China |
| Abstract: | The main objective of this paper is to extend previous results on Halanay inequality for impulsive delayed dynamical systems. Based on the Razumikhin technique, a generalized Halanay differential inequality on impulsive delayed dynamical systems is analytically established. Compared with some existing works, the distinctive feature of this work is that it can be used to stabilize an unstable delayed dynamical system via impulses. The generalized Halanay inequality may be applied to secure communication systems, and a numerical example is given for illustrating and interpreting the theoretical results. |
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