New approaches on stability criteria for neural networks with interval time-varying delays

Keywords: Neural networks Time-varying delays Stability Lyapunov method a b s t r a c t This paper concerns the problem of delay-dependent stability criteria for neural networks with interval time-varying delays. First, by constructing a newly augmented Lyapunov– Krasovskii functional and combining with a reciprocally convex combination technique, less conservative stability criterion is established in terms of linear matrix inequalities (LMIs), which will be introduced in Theorem 1. Second, by taking different interval of integral terms of Lyapunov–Krasovskii functional utilized in Theorem 1, further improved stability criterion is proposed in Theorem 2. Third, a novel approach which divides the bounding of activation function into two subinterval are proposed in Theorem 3 to reduce the conservatism of stability criterion. Finally, through two well-known numerical examples used in other literature, it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea. Recently, neural networks have been found successful applications in various fields including image and signal processing , pattern recognition, fault diagnosis, associative memories, fixed-point computations, combinatorial optimization, and other scientific areas (for instance, see [1–4]). Since these applications heavily depend on the dynamic behavior of the equilibrium point, the stability analysis of the equilibrium points of the designed network has been one of important issue. In the implementation of neural networks, time delays frequently occur due to the finite switching speed of amplifies and may cause instability or oscillation of neural networks. Therefore, considerable efforts have been done to asymptotic stability analysis of neural networks with time-delays [5–36]. Especially, delay-dependent stability analysis has been investigated by many researchers [18–36] since it is well known that delay-dependent stability criteria are generally less conservative than delay-independent ones when the sizes of time-delays are small. In the field of delay-dependent stability analysis, an important index for checking the conservatism is to find maximum delay bounds such that the asymptotic stability of the designed network can be guaranteed for any admissible delays less than maximum delay bounds. Thus, how to choose Lyapunov–Krasovskii functional and obtain an upper bound of time-derivative of it play key roles to increase the feasible region of stability criteria. Since Li et al. [21] pointed that the stability conditions are hardly improved by using the same Lyapunov–Krasovskii functional , delay-partitioning approach, which was firstly introduced by Gu [38], has been attracted by many researchers. One of the 0096-3003/$-see front …