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We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely-studied delayed neural network models with almost periodic self-inhibitions, interconnections weights and external inputs. We prove that diagonal dominant conditions can guarantee the existence and uniqueness of an almost periodic solution as well as its global exponential stability. As special cases, we derive a series ofdoi:10.1162/neco.2008.10-06-364 pmid:18085989 fatcat:qsd5xrwthrhwdmq3zff44rd4nu