Analysis of Distinguishability of Linear Descriptor Control Systems using Drazin Inverse

Abstract

This article aims to provide the equivalent criteria for the distinguishability
of linear descriptor systems (LDS). Regularity of the matrix pencil,
which, loosely speaking, guarantees the existence, and uniqueness of the solution
of LDS for any inhomogeneity, is required in this article. A characterization of
observability for LDS in terms of distinguishability is given. The Laplace transform
together with the Cayley-Hamilton theorem exploited to derive Hautustype
criteria for the distinguishability. In addition, we present examples of
distinguishable systems.