Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays

Abstract

This paper focuses on the exponential convergence of impulsive inertial complex-valued neural networks with time-varying delays. The system can be expressed as a first order differential equation by selecting a proper variable substitution. By constructing proper Lyapunov–Krasovskii functionals and using inequality techniques, some delay-dependent sufficient conditions in linear matrix inequality form are proposed to ascertain the global exponential convergence of the addressed neural networks with two classes of complex-valued activation functions. The framework of the exponential convergence ball domain in which all trajectories converge is also given. Meanwhile, the obtained results here do not meet that the derivatives of the time-varying delays are less than one and there are also no limit to the strength of impulses. The methods here can also be applied to deal with multistable and monostable neural networks because of making no hypotheses on the amount of the equilibrium points. Finally, two examples are given to demonstrate the validity of the theoretical results.