On the Stability of Some Exponential Polynomials

This paper studies elementary transcendental equations of the type z 2qpzq q.etzqrzns0, where p, q, rgR, t , p)0, qG0, r/0, ns0, 1, 2. We are mainly interested in the case ns0 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 ns1, 2. The proofs are carried by elementary arguments independent of usual tools