Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

Abstract

This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.

Exponential Stability of Switched Neural Networks with Partial State Reset and Time-Varying Delays

“…It is clear that the partial state reset proposed in this paper can take pinning impulses as a special case. Thus, the partial state reset is more tough and realistic than the impulses considered in [3,24,35,48,49].…”

“…Note that there are some results on the stability of switched systems with impulsive effects, where the system state was reset at impulsive instants [24,[33][34][35][36]. The switched system with state reset is usually modeled as an impulsive differential or impulsive functional differential system [30,37,38].…”

“…(1) SNNs with partial state reset is proposed in this paper, where the partial state reset is more realistic than pinning impulses and time-varying impulses considered in the existing literature [24,35,48,49]. What is more, stable subsystems, unstable subsystems, and timedelay effects are also taken into account, which renders our SNNs model more practical.…”