Normalized Difference Model of the Descriptor Control System

A difference model approximating a semi-linear descriptor control system with continuous time is studied to enable further application of the results in developing neural networks. An algorithm has been developed to transform the implicit difference equation so that, in its linear part, the original regular characteristic pencil of two matrices is converted into a normalized pencil with an identity matrix as the free term and a certain "informational" matrix T associated with the spectral parameter. One of the key steps in the algorithm involves reducing the matrix T to its Jordan form with a special arrangement of Jordan blocks. An example of a descriptor dynamic system in an electrical network is considered.