On the Stability of Linear Delay-Differential Algebraic Systems: Exact Conditions via Matrix Pencil Solutions

In this paper we study the stability properties of a class of linear systems expressed by semi-explicit delay differential algebraic equations, that is a system of functional differential equations coupled with a system of (continuous-time) difference equations. We show that the stability analysis (delay-independent, delay-dependent, crossing characterization) in the commensurate delay case can be performed by computing the generalized eigenvalues of certain matrix pencils, which can be executed efficiently and with high precision. The results extend previously known work on retarded, neutral, and lossless propagation systems, and demonstrate that similar stability tests can be derived for such systems