Regulatory processes and history dependent behavior appear in many dynamical systems in nature and technology. For modeling regulatory processes, hybrid systems offer several advances. From this point of view, to observe the capability of hybrid systems in a history dependent system is a strong motivation. In this book, I have developed functional hybrid systems which exhibit memory dependent behavior such that the dynamics of the system is determined by both the location of the state vector and the memory. This property was explained by various examples. I have used the hybrid system with memory formalization in modeling gene regulatory network of human immune response to Influenza A virus infection. I have investigated the sensitivity of the piecewise linear model with memory. I have introduced how the model can be developed in future. This book should help shed some light on this useful and advantageous model and should be benefical to anyone who is interested in hybrid systems.