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Lyapunov functionals and Lyapunov functions coupled with the Razumildiin technique are still the most popular tools in studying the stability of large-scale retarded nonlinear systems. However, it is generally difficult to construct Lyapunov functionals or functions that satisfy the strong conditions required in the classical stability theory. In this paper, we show that for some delay differential systems such as additive neural networks with delays, we can weaken the condition that the Lyapunov functional or function is positive definite, by using the equivalence between the state stability and the output stability. We apply our general theory to obtain some new stability conditions for cellular neural network models. It is represented that it is easy to construct Lyapunov functionals or functions satisfied conditions of our theorems. [ABSTRACT FROM AUTHOR]

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. [ABSTRACT FROM AUTHOR]