Mapping Discrete-time Models for Descriptor-systems with Consistent Initial Conditions

Discretization of a regular continuous-time descriptor-system, whose initial condition is consistent with its input, is considered using a general mapping method presented in our previous paper. The proposed mapping discrete-time model is shown to be a proper discretization under the definition explained in the paper. This assures that the response of the mapping model approaches that of the continuous-time descriptor system as the sampling period approaches zero. The consistency of initial conditions for the discrete-time model is also studied and the long-standing issue of ambiguities surrounding irregularities of discrete-time responses at the initial time are clarified with a simple solution. A proper range of design parameters are investigated and their suitable choices suggested. To illustrate the use of the proposed method, a simple circuit that cannot be expressed in the ordinary state-space form is considered. Its responses to a sinusoidal input when started from the consistent and inconsistent initial conditions are simulated to show that the irregularities at the initial time can be overcome easily. The proposed technique provides a convenient simulation and design environment for handling discrete-time systems in a unified manner with consistency and ease.