Numerical and Analytic Analysis of Implicit Differential Equations and Their Application to Control and Circuit Problems

摘要

Results on the numerical and analytic solution of implicit systems of differential equations and their application to circuit and control problems were developed. In particular, the first general algorithm for the linear time varying case was developed along with an analysis of how to apply it to certain control problems. New structure theorems provide insight on the convergence of backward formulas and guidelines for their use.