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Eigenvalue and stability of singular differential delay systems. (English) Zbl 1063.34052

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.

MSC:

34K06 Linear functional-differential equations
34K20 Stability theory of functional-differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
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