We show that uniformly global asymptotic stability for a family of ordinary diierential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables.

Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, A novel criterion for the global asymptotic stability of cellular neural networks with time-varying discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily...

K e y w o r d s N o n l i n e a r systems, Cascade systems, Discrete-time systems~ Local asymptotic stability, Global asymptotic stability.

We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary diierential equations are equivalent to uniformly global exponential stability and a nonlinear H1 estimate, respectively , under suitable nonlinear changes of variables.

In this paper, the global asymptotic stability of second-order neutral type Cohen-Grossberg neural networks with time-varying delays are investigated. First, by choosing properly variable substitution the system is transformed to first-order differential equation. Second, some sufficient conditions which can ensure the existence and global asymptotic stability of equilibrium point for the syste...

In this paper‎, ‎a bidirectional ring network with three cells and different time delays is presented‎. ‎To propose this model which is a good extension of three-unit neural networks‎, ‎coupled cell network theory and neural network theory are applied‎. ‎In this model‎, ‎every cell has self-connections without delay but different time delays are assumed in other connections‎. ‎A suitable Lyapun...

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained. Keywords—Difference equations, stability, unstable, global asymptotic behavior.