New impulse(noncausality) test for descriptor systems by Möbius transformation

Descriptor systems (DSs) are usually used to model very-large-scale integration (VLSI) circuit systems and multibody dynamics macromodeling. The analysis of DSs, however, is much more complicated than linear time-invariant (LTI) systems due to the poles at infinity. Mo¨bius transformation (MT) provides a way to transform poles at infinity to finite poles and largely facilitates the reuse or adaptation of the standard techniques for LTI system to analyze DSs. Nonetheless, MT is well known in the literature and its potential use is currently less appreciated in the analysis of DSs. This paper gives a new way to the impulse (noncausality) test using the properties of the transformed LTI systems by MT. Moreover, the applications to the analysis of controllability, observability and regularity are given. Numerical examples are included to show the effectiveness of the proposed method.