Generalized passivity of coupled neural networks with directed and undirected topologies

The generalized passivity is discussed for coupled neural networks (CNNs) with directed and undirected topologies, respectively. Firstly, some generalized passivity definitions are proposed for general systems, in which output and input vectors may have different dimensions. By exploiting concepts of passivity and matrix theory, several criteria are established to guarantee the generalized passivity of CNNs with directed and undirected topologies.  However,  in many circumstances, CNNs with known coupling weights is not passive. Therefore, some control schemes for updating the coupling weights are also presented. By using these adaptive control schemes, several criteria for ensuring network passivity are derived. In addition, two simulation examples are presented to show the correctness of proposed passivity criteria.