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Remarks concerning the asymptotic stability and stabilization of linear delay differential equations. (English) Zbl 0579.34052

Summary: This note concerns the asymptotic stability for all values of the delays of controlled and uncontrolled linear delay differential equations. In the case of uncontrolled systems it is shown by example that structural considerations must be accounted for. In the controlled case, although arbitrary pole placement may not be possible, there is an algorithm which sometimes reduces the spectrum of the feedback system to one which is finite and is contained in the left half plane.

MSC:

34K20 Stability theory of functional-differential equations
34H05 Control problems involving ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34K05 General theory of functional-differential equations
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