Enhanced gradient calculation method for MADCADS

MADCADS (Model and Data-Oriented Computer Aided Design System) is a software package that employs numerical search-based algorithms in order to improve the characteristics of a given controller. The search-based nature of the code requires the calculation of many various gradients with respect to the controller parameters. New mathematical constructs are developed here which lead to more reliable and maintainable code. Specifically, a special representation for the derivative of a certain class of matrix-valued functions with respect to another matrix is presented. Algebraic and operator theoretic concepts are developed including a chain rule operation which is analogous to that used in standard calculus.<>