Finite-time Stability Of Neural Networks Research Articles

Novel conditions for finite-time stability of neural networks with time varying delay

In this paper, the problem of finite-time stability of neural networks with time varying delay is considered by using improved reciprocally convex inequalities and some integral inequalities, combined with Wirtinger’s inequalities and some useful integral inequality. New sufficient conditions for finite-time stability are established to guarantee finite-time stability for the system are given in terms of linear matrix inequalities(LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

In this paper, the impulsive effects on the finite-time stability of neural networks with time-varying delay are considered. Several novel criteria which govern the systems considered are finite-time stable are obtained by the idea of Lyapunov–Krasovskii functional and the average impulsive interval method. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities which can be easily checked by Matlab LMI toolbox. The results proposed show that the model can achieve stable in finite time with stabilizing impulsive effects on one hand, and it can preserve the finite-time stability property in presence of destabilizing impulses on the other hand. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

Nonsmooth finite-time stabilization of neural networks with discontinuous activations

This paper is concerned with the finite-time stabilization for a class of neural networks (NNs) with discontinuous activations. The purpose of the addressed problem is to design a discontinuous controller to stabilize the states of such neural networks in finite time. Unlike the previous works, such stabilization objective will be realized for neural networks when the activations and controllers are both discontinuous. Based on the famous finite-time stability theorem of nonlinear systems and nonsmooth analysis in mathematics, sufficient conditions are established to ensure the finite-time stability of the dynamics of NNs. Then, the upper bound of the settling time for stabilization can be estimated in two forms due to two different methods of proof. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.