Fixed-time control of delayed neural networks with impulsive perturbations

Abstract

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis.

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

“…Set V(t) = V(t, x(t)) and (t) = (t − t 0 ), where scalar > 0 and we can observe that (t) ∈ K 0 . By Corollary 2, we obtain that condition (7) can be reduced by Moreover, if there is a satisfying (25), and then we have…”

“…We can find earlier works on impulsive systems in the works of Lakshmikantham et al and Benchohra et al The impulsive system is generally regarded as an important type of hybrid system. Specifically, the impulsive system is composed of three parts, ie, continuous evolution, discrete evolution, and an impulsive rule, determining when the impulses happen . The stability analyses of impulsive systems have been extensively investigated by many investigators .…”

“…Specifically, the impulsive system is composed of three parts, ie, continuous evolution, discrete evolution, and an impulsive rule, determining when the impulses happen. [21][22][23][24][25][26] The stability analyses of impulsive systems have been extensively investigated by many investigators. [12][13][14][27][28][29] Moreover, Hespanha et al 14 and Chen and Zheng 30 have presented the notions of ISS and iISS of (delayed) impulsive systems, and some sufficient criteria based on Lyapunov methods for above characters have been derived.…”

Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

“…However, the recent studies and experiments on neural network models indicated that impulsive control is more effective in their numerous applications mainly because it allows the control actions only at some discrete instances. That is why different classes of impulsive control neural networks, including CNNs, have been massively studied in the literature [49][50][51][52].…”

pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

“…Motivated by some ideas and methods in [16,[32][33][34][35][36][37][38][39][40]46], we are to investigate the stability of a class of p-Laplacian diffusion T-S fuzzy system via variational methods that are different from those of existing literature related to reaction-diffusion fuzzy systems.…”