Global robust stability analysis of neural networks with multiple time delays

Abstract

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By employing suitable Lyapunov functionals, we derive a set of delay-independent sufficient conditions for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature. One of our main results is shown to improve and generalize a previously published result. Other results proved to establish a new set of robust stability criteria for delayed neural networks.Index Terms-Delayed neural networks, equilibrium and stability analysis, Lyapunov functionals.

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

“…Therefore, by (17) and (18) neural network (3) is asymptotically stable. The proof is thus completed.…”

“…Note that compared with (5), (17) and (18) need not require μ < 1; they can be applied to fast time-varying delays as well as slow ones, only if μ is known. For the case when μ is unknown, setting Q = Q 1 = 0 we have a delay-derivative-independent criterion as follows.…”

“…For the former, we refer the readers to [4,11,17,21,25] and the references therein. 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.…”

Lag Synchronization of Switched Neural Networks via Neural Activation Function and Applications in Image Encryption

“…This means the conditions about stability criteria derived for switched neural networks in [26] and [27] are more restrictive than those in Theorem 1. Meanwhile, these results can only guarantee the globally asymptotical stability of the switched lag synchronization error system (9).…”

New sufficient criteria for global robust stability of neural networks with multiple time delays

“…Theorem 4 (32). Let f ∈ K. Then, the neural network model (2) is globally asymptotically robust stable, if…”