New results on stability analysis of neural networks with time-varying delays

Novel Delay-Dependent Stability Results for Neural Networks with Time-Varying Delays

“…To begin with, no system transformation is performed to the original system; thus, there is no need to overbound the cross-product terms induced by the transformation. In addition, V 4 (x) is included in the Lyapunov functionalṼ (x t ), so that when estimatinġṼ (x t ) we are able to reserve not only the integral − t t−τ (t)ẋ (α) T Zẋ(α) dα but also − t−τ (t) t−τẋ (α) T Zẋ(α) dα, which was often ignored in previous papers [10]. Finally, as the two integrals of˙Ṽ (x t ) are dealt with by using free-weighting matrix methods, the resulting terms τ (t)NZ −1 N T and (τ − τ (t))MZ −1 M T are not so enlarged as in [8], but are kept as they are and handled with convex combination methods.…”

“…Since these criteria are generally more conservative than delay-dependent ones, especially when the size of the delay is small, delay-dependent stability has been developed with considerable interest. For RNNs with a constant delay, delay-dependent results were obtained in [16,22,23], while delay-dependent criteria were reported for the case of time-varying delays in, e.g., [6,8,10,24]. For RNNs with distributed delays, delay-dependent stability was addressed in [5,13,15].…”

Improved delay-dependent stability analysis for uncertain stochastic neural networks with time-varying delay

“…The upper bound of s for various l from Theorem 2 and those in [17] and [18] are listed in Table 2. It is also clear that the obtained upper bounds of s in this brief are better than in [17] and [18], which guarantee the asymptotic stability of neural networks.…”

“…Therefore, the stability of delayed neural networks has aroused considerable interests in recent years, since the dynamic behavior of neural network often involves time delays, which may bring the instability of systems, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein. In these literatures, stability results can be classified into two types: delay-independent stability criteria and delay-dependent stability criteria.…”

Novel Robust Stability Criteria for Uncertain Stochastic Neural Networks with Time-Varying Delay

“…Choosing Lyapunov-Krasovskii functional V (x(t),t) = V 1 (x(t),t) + V 2 (x(t),t) + V 4 (x(t),t), where V 1 (x(t),t),V 2 (x(t),t), and V 4 (x(t),t) are defined in (13). By Assumption 2.2, it is well known that there exist diagonally matrices D 1 0, D 2 0 such that the following inequalities hold…”