Invariance principle and complete stability for cellular neural networks

In applications of classification of patterns, image processing, associative memories etc, the complete stability of cellular neural networks (CNNs) plays an important role. Invariance principles based on the Lyapunov functions and functionals are still the most advantageous theory to analyze the complete stability. However, one difficulty in applying classical invariance principles to the complete stability is to prove that the largest invariant set consists of equilibrium points. In this paper, we present one invariance principle to analyze the complete stability. We can avoid the difficulty of proving that the largest invariant set is constituted of equilibrium points in discussing some sufficient condition for complete stability of CNNs by using this invariance principle.