Mean-square exponential input-to-state stability of stochastic inertial neural networks

Abstract

By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the mean-square exponential input-to-state stability on the addressed model, which generalizes and refines the recent results. In addition, an example with numerical simulation is carried out to support the theoretical findings.

Mean‐square exponential input‐to‐state stability of stochastic delayed recurrent neural networks with local Lipschitz condition

“…Obviously, Assumption 1, local Lipschitz condition, is weaker than uniform Lipschitz one given in [4–29]. Hence, our results have improved and generalized some existed ones of [4–29]. Moreover, we shall show that the main result of [19] is a particular case of this paper.…”

“…To our knowledge, rare researchers have considered stochastic delayed recurrent neural networks without uniform Lipschitz condition. Obviously, Assumption 1, local Lipschitz condition, is weaker than uniform Lipschitz one given in [4–29]. Hence, our results have improved and generalized some existed ones of [4–29].…”

“…Up until now, many researchers have deeply studied the stability of stochastic delayed recurrent neural networks (1.1), and the mainstream results can fall into two categories. One is the traditional stability, such as asymptotic stability [4][5][6], exponential stability [7][8][9][10][11][12][13][14][15][16], and almost sure exponential stability [17,18], and the other is the untraditional stability: input-to-state stability [19][20][21][22][23][24][25][26][27][28][29], where the states of stochastic neural networks do not converge to the equilibrium point as time goes to infinity. Unfortunately, both stability results of stochastic delayed recurrent neural networks (1.1) depend on the conditions that the activation functions satisfy uniform Lipschitz condition, which is somewhat restrictive.…”