Linear descriptor systems and their exact discrete-time model

The present paper deals with the development of a discretization technique for linear systems expressed in descriptor form, called the descriptor system. The descriptor form is capable of handling systems that are not possible using the more standard state-space expression, such as those involving order changes and algebraic constraints among internal variables. The main aim of this paper is to derive, for a descriptor-system, an exact discrete-time model whose response matches exactly that of the continuous-time original with its input being held constant via a zero-order-hold, at all discrete-time instants for any sampling interval. Such a model is developed for the case where the so-called descriptor matrix is non-singular and for the case where it is singular.