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On the Stability of Some Exponential Polynomials

✍ Scribed by Margarete Baptistini; Plácido Táboas

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
195 KB
Volume
205
Category
Article
ISSN
0022-247X

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✦ Synopsis

This paper studies elementary transcendental equations of the type z q pz q . z n q e q rz s 0, where p, q, r g ‫,ޒ‬ , p ) 0, q G 0, r / 0, n s 0, 1, 2. We are mainly interested in the case n s 0 for which a characterization of stability is accomplished; that is, we state a necessary and sufficient condition for all the roots to lie to the left of the imaginary axis. Also a characterization of stability independent of delays is given. Sufficient conditions for instability are stated for the cases n s 1, 2. The proofs are carried by elementary arguments independent of usual tools.

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