The general goal of this research project is the development of a better understanding of the fundamental nature of discrete time circuits, fault diagnosis in analog circuits and nonlinear transistor networks and their properties, and the development of new mathematical techniques for their analysis and design. Utilization of results from the proposed work is expected in important applications such as the checkout and maintenance of complex electronic circuit boards and in the development of analytical methods for solving related problems. The research will also contribute significantly to the training of new researches and result in PhD dissertations.