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Characteristic matrices for linear periodic delay differential equations. (English) Zbl 1229.34115

Authors’ abstract: R. Szalai, G. Stépán and S. J. Hogan [SIAM J. Sci. Comput. 28, No. 4, 1301–1317 (2006; Zbl 1118.37037)] gave a general construction for characteristic matrices for systems of linear delay differential equations with periodic coefficients. First, we show that matrices constructed in this way can have a discrete set of poles in the complex plane, which may possibly obstruct their use when determining the stability of the linear system. Then, we modify and generalize the original construction such that the poles get pushed into a small neighborhood of the origin of the complex plane.

MSC:

34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations
34K08 Spectral theory of functional-differential operators
34K13 Periodic solutions to functional-differential equations

Citations:

Zbl 1118.37037

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