On the boundedness of cellular neural network trajectories

The paper revisits the boundedness for the trajectories of cellular neural networks (abbreviated as CNNs) and proposes a refined approach to this property. Our refinement envisages sufficient conditions for the existence of invariant sets with respect to the CNN dynamics. First, we construct a general framework which considers bounded sets with arbitrary time-dependence. Then we focus on the particular type of exponentially contractive sets. In both approaches, we provide results for the general case of non-symmetric sets. Finally we show that for some types of contractive sets, the invariance condition can be tested by well-known instruments of matrix algebra. An example illustrates the applicability of the theoretical developments.