Stability in Lagrange sense for Cohen–Grossberg neural networks with time-varying delays and finite distributed delays

New LMI-based Criteria for Lagrange Stability of Cohen-Grossberg Neural Networks with General Activation Functions and Mixed Delays

“…In the literature [24,25], the results were obtained under the condition that the timevarying delays are continuously differentiable, of which the derivative was bounded and smaller than one, and the activation functions were limited on bounded and monotonically non-decreasing. It is needed to point out that, in this paper, the presented results do not need the conditions mentioned above.…”

“…Hence, the study of Lagrange stability depends on the existence of global exponentially attractive set, not considering uniformly bounded of the system. However, in the reference [18,[21][22][23][24][25], the Lagrange stability was determined by both uniformly bounded and globally exponentially attractive set. …”

“…It is worth to mention that unlike Lyapunov stability, Lagrange stability refers to the stability of the total system, rather than the stability of the equilibriums, because the Lagrange stability is considered on the basis of the boundedness of solutions, which depend on the existence of global attractive sets (see [12,18,19,[21][22][23][24][25]). We also note that Lagrange stability has attracted phenomenal worldwide attention.…”

“…Then [21] and [22] continued to probe further into the Lagrange stability for neutral type and periodic recurrent neural networks along the methods in [18,19], respectively. In [24,25], Lagrange stability is discussed for Cohen-Grossberg neural networks (CGNNs) with time-varying delays and finite distributed delays. To our best knowledge, these results of Lagrange stability analysis for neural networks depend mainly on Lyapunov-like functions, and there are few results made on it by LMIs [32].…”

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

“…This is possible only if there are multiple equilibria with some being unstable. As we know, Lagrange stability is one of the most important properties in multistability analysis of the total system which does not require the information of equilibriums [50][51][52][53][54]. The boundedness of solutions and the existence of globally attractive sets lead to a total system concept of stability: (asymptotic) Lagrange stability [55,56].…”