Mean square exponential stability of uncertain stochastic delayed neural networks

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

“…However, by our Theorem 3.3 and using Matlab LMI Toolbox, for h 1 = 0 it is found that the equilibrium solution of uncertain stochastic neural networks (1) is robustly exponentially stable in mean square for any arbitrarily large h 2 (as long as numerical computation reliable). Therefore, for this example, the results given in this paper are less conservative than those in [29] and [3]. …”

“…This shows that the established results in this paper is finer than the previous results since the stability region is valid upto the upper bound 4.4690 instead of 2.2471 in [29]. In order to compare the results in this paper with those in [3,29], we assume that the activation functions satisfy (A2) with c 1 = c 2 = c 3 = 0 andc 1 = 1.2,c 2 = 0.5,c 3 = 1.3. When the time-varying delay is differentiable and μ = 0.85, by using Theorem 3.1 in this paper, Theorem 1 in [29] and Theorem 1 in [3], we obtain the maximum allowable upper bound of τ (t) as h 2 = 9.7377, h = 9.6876, and h = 7.7377, respectively.…”

“…When the time-varying delay is differentiable and μ = 0.85, by using Theorem 3.1 in this paper, Theorem 1 in [29] and Theorem 1 in [3], we obtain the maximum allowable upper bound of τ (t) as h 2 = 9.7377, h = 9.6876, and h = 7.7377, respectively. When the time-varying delay may not be differentiable, that is, μ is unknown, by using Theorem 2 in [29] and Theorem 2 in [3], the maximum allowable upper bounds are h = 2.2379 and h = 2.3514, respectively. However, by our Theorem 3.3 and using Matlab LMI Toolbox, for h 1 = 0 it is found that the equilibrium solution of uncertain stochastic neural networks (1) is robustly exponentially stable in mean square for any arbitrarily large h 2 (as long as numerical computation reliable).…”

“…In order to compare the results in this paper with those in [3,29], we assume that the activation functions satisfy (A2) with c 1 = c 2 = c 3 = 0 andc 1 = 1.2,c 2 = 0.5,c 3 = 1.3. When the time-varying delay is differentiable and μ = 0.85, by using Theorem 3.1 in this paper, Theorem 1 in [29] and Theorem 1 in [3], we obtain the maximum allowable upper bound of τ (t) as h 2 = 9.7377, h = 9.6876, and h = 7.7377, respectively. When the time-varying delay may not be differentiable, that is, μ is unknown, by using Theorem 2 in [29] and Theorem 2 in [3], the maximum allowable upper bounds are h = 2.2379 and h = 2.3514, respectively.…”

“…Therefore, it is of practical importance to study the stochastic effects on the stability property of delayed neural networks, see for example [3][4][5][6]11,16,18,19,23,27,29]. Also, there are systems which are with some nonzero delays, but they are unstable without delay [7,8,30].…”