Neurons are characterized by an electric potential which is established between their inside and outside media. They exhibit specific voltage fluctuations, in response to strong enough current impulses, called action potentials. In this work, a bang-bang controlled bilinear system (BLS) is derived to approximate the generation of a simple neuron's action potential. The shape of the response, as well as the timing seem to be useful for experimental planning and interpretation to neural physiologists. The BLS-model has the potential to aid the design and fabrication of commercial neural networks for communication, control and computing. In this manner, a variable-structure membrane impedance, such as exhibited by a stable focus and a saddle point in state space, and/or other modes, arises naturally. Added positive and negative stimuli, such as from other neurons, have the capability to alter the voltage across the inside and the outside media of the neuron and elicit an advanced or delayed response in the action potential. Such latency is significant as noted above, and is an active area of experimental research. The response shape and the timing with respect to some other event(latency} are related to experimental data. This simple model is compared to the complex and highly celebrated Hodgkin-Huxley model for the squid giant axon. The bang-bang feedback control is given a biological interpretation of sodium and potassium ion channels in this axon, that yields a variable-structure membrane impedance. / Graduation date: 2000