Global Asymptotic Stability of Impulsive CNNs with Proportional Delays and Partially Lipschitz Activation Functions

Abstract

This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation $v_i(t)=u_i(e^t)$, the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.