Eigenvalue and stability of singular differential delay systems
The author is concerned with the relationship between eigenvalues and stability for linear delay differential algebraic equations with constant coefficients and of the form \[ E\dot x(t)=Ax(t)+Bx(t-\tau) \] with a singular matrix \(E\). It is shown that if the matrix pencil \((A,E)\) is regular and \(BEE^d=EE^dB\) (where \(E^d\) denotes the Drazin inverse), the familiar results including the exponential estimate remain valid.
differential algebraic equation with delay
scientific article; zbMATH DE number 2105442