Stability analysis on state-dependent impulsive Hopfield neural networks via fixed-time impulsive comparison system method

Abstract

Abstract This paper aims at the stability problem of state-dependent impulsive Hopfield neural networks. Under well-selected conditions, we transform the considered neural networks into the analog with fixed-time impulses, namely, fixed-time impulsive comparison systems. By means of the stability theory of fixed-time impulsive systems, we establish several sufficient conditions for the exponential stability of state-dependent impulsive Hopfield neural networks. The present results show that state-dependent impulsive Hopfield neural networks can remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem. We illustrate the validity of the theoretical results by three numerical examples.