id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3848	Mingxin, Zha; Wenxiao, Si; Tao, Xie	Robust Exponential Stability of Recurrent Neural Networks with Deviating Argument and Stochastic Disturbance	2020	13	.pdf	application/pdf	4390	277	72	For t0 ≤ t ≤ t0 + 2ρ, from (1), we have E‖y(t)− x(t)‖2 = E‖ ∫ t t0 −A(y(s)− x(s)) Thus, considering (23) and (24), for t ≥ t0 − α+mρ, ‖y(t; t0, y0)‖ = ‖y(t; t0 + (m− 1)ρ, y(t0 + (m− 1)ρ; t0, y0))‖ ≤ exp(−ρτ)‖y(t0 + (m− 1)ρ; t0, y0)‖ ≤ exp(−mρτ)‖y0‖ Consequently, when t > t0−α+ρ, the positive integer m that satisfies t0−α+(m−1)ρ ≤ t ≤ t0 − α+mρ, ‖y(t; t0, y0)‖2 ≤ exp(−τ(t− t0))exp(τ(ρ− α))‖y0‖2 (25) Obviously, (25) also holds for t0 ≤ t ≤ t0 − α+ ρ.	cache/ejpam-3848.pdf	txt/ejpam-3848.txt