Finding the stability and sensitivity of large sampled systems

The stability of a large sampled system is examined by finding the eigenvalues of the difference equation that describes the system. The derivatives of these eigenvalues with respect to the system parameters are found to give the sensitivity of the system to the various parameters. A method of finding the difference equations for the system is described which is based on exponentiating the matrix of the system with the samplers open. The problem of multiple eigenvalues is considered, and a block-form solution is used to determine the nature of the multiplicity of the multiple eigenvalues.