Finite-Time Stability and Stabilization of Impulsive Stochastic Delayed Neural Networks With Rous and Rons

Abstract

This paper mainly tends to investigate finite-time stability and stabilization of impulsive stochastic delayed neural networks with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs). Firstly, by constructing the proper Lyapunov-Krasovskii functional and employing the average impulsive interval method, several novel criteria for ensuring the finite-time stability of impulsive stochastic delayed neural networks are obtained by means of linear matrix inequalities (LMIs). Then, some conditions about the state feedback controller are derived to ensure the finite-time stabilization of impulsive stochastic delayed neural networks with ROUs and RONs. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results. INDEX TERMS Finite-time stability and stabilization, impulsive stochastic neural networks, average impulsive interval, time-varying delay, ROUs, RONs.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

“…Currently, boundedness and the Lipschitz conditions are the two most common assumptions. In studies [31,32,35,37,42,[45][46][47]51] and [10], the activation functions are assumed to be in the real number field and quaternion field, respectively. In studies [30,33,36,38,39,41,43,44,48,49,53] and [14][15][16][17][18][19][20][21][22]26,29,34], the activation functions are assumed to meet the Lipschitz condition in the real field and quaternion field, respectively.…”

“…The delay phenomenon may reduce the convergence rate to equilibria of NNs and even cause considerable damage to the stability of systems. The delay phenomena of NN models have been examined in the literature, including fixed delays [30], variable delays [9][10][11][12][13][21][22][23][24][25][26][31][32][33][34][35][36], infinitely distributed delays [21,33,34,36], and neutral delays [12]. Uncertain interference factors are also unpreventable in NNs.…”

Finite-Time Annular Domain Stability and Stabilization of Regime-Switching Jump Diffusion System

“…Regime-switching jump diffusion processes can be seen as a jump diffusion process in a stochastic environment, where the evolution of the stochastic environment is modeled by continuous-time Markov chain, or more generally, a continuous-state-dependent switching process with a discrete state space [17]. In order to simulate more systems, many scholars have considered and studied stochastic systems [4], [8]- [15], [22], and also studied many properties of the regime-switching jump diffusion system, such as asymptotic stability in probability, finite-time annular domain stability in the sense of expectation and so on.…”