A generalized Halanay inequality on impulsive delayed dynamical systems and its applications

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.

► A generalized Halanay differential inequality is derived.
► By using the inequality, we can stabilize an unstable dynamical system via impulses.
► The results are applied to chaos-based secure communication systems.
► The results may develop an effective impulsive control strategy.