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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.

34K06Linear functional-differential equations
34K20Stability theory of functional-differential equations
34A09Implicit equations, differential-algebraic equations
Full Text: DOI
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