Sensitivities of large, multiple-loop control systems

This paper describes a method of analyzing large, multiple-loop control systems which can be represented by simultaneous, linear, first-order, differential equations. The eigenvalues of the system are found using the QR transform. Next, the sensitivities of these eigenvalues to the system's parameters are found from the normal and transposed eigenvectors of the system. Results from a 51st-order system to which this method has been applied are given as an example.