On bi-proper mapping discretization of a regular descriptor system

A mapping discrete-time model is proposed for discretizing a continuous-time regular descriptor-system. The model is developed based on the Kronecker form, where the system is decomposed into the exponential mode and the static/impulsive mode. While discretization of exponential modes does not require modification of a relative-degree, the static and the impulsive modes need one for their bi-properization. The proposed mapping model is suitable for implementing non-proper systems in digital form, such as a derivative controller. Simulations are carried out for an electric circuit modeled as a descriptor system containing only the impulsive mode, to show the veracity of the proposed method.