Sensitivity analysis of large linear networks using symbolic programs

Partial derivatives of a network function H(x) with respect to the parameters x=(x₁, x₂,,,,x_n) are useful in the design of linear networks by optimization and in tolerance analysis. Existing methods for calculating these derivatives include the sensitivity network method, the adjoint network method, and the symbolic network function method. In recent years, several new methods have been developed for symbolic analysis of large linear networks. The new methods express the symbolic answer in the form of a sequence of expressions. The author investigates the calculation of the derivatives based on the sequence of expressions. Two methods are presented. The first method derives another sequence of expressions for each sensitivity function. The second method utilizes a 3-point formula to determine the coefficients in the bilinear function from which the sensitivity function is calculated