Formation of the Coefficient Matrix of a Large Dynamic System

The coefficient matrix for the set of first-order differential equations that describe a dynamic system is formed from the block diagram or equations that describe the system. The method for accomplishing this is described in terms of matrix equations. Then the derivative of this coefficient matrix with respect to one of the system parameters is found in terms of the matrices used to form it. The coefficient matrix and its derivative can be used to find the eigenvalues of the system and the sensitivities of the eigenvalues to the system's parameters.