New distributions properties and applications in digital control

In this paper, the definition, modeling and simulation of elementary Swartz distributions and their properties are first considered. Using this theory a new theorem and property were demonstrated, modeled and simulated with significant application examples. The paper presents an extremely useful application for digital control of power electronics. The proposed solution uses the properties and the new theorem in order to solve complex nonlinear equations to produce appropriate digital control signals. This solution can be easily coded in a hardware description language and downloaded in an ASIC chip as part of an embedded controller.