The Transfer Matrix of Differential-Algebraic Equations

The article deals with a few questions about the transfer matrix of a system of linear differential-algebraic equations (DAEs). Considering systems with a regular matrix pencil, we obtain the form of the transfer matrix whose minimal realization we propose to seek in the class of DAEs with the simplest internal structure: separated differential and algebraic components. To construct the state space of the algebraic subsystem, we use the skeleton decomposition of the matrix of coefficients of the corresponding matrix polynomial. For transfer matrices with parametric uncertainty we obtain existence conditions and propose an algorithm for constructing a minimal realization of the polynomial matrix as an algebraic subsystem with coefficients continuously depending on the parameters.