On the stability of some exponential polynomials

Abstract

This paper studies elementary transcendental equations of the type (z2+pz+q)eτz+rzn=0, wherep,q,r∈ R , τ,p>0,q≥0,r≠0,n=0,1,2. We are mainly interested in the casen=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 casesn=1,2. The proofs are carried by elementary arguments independent of usual tools. © 1997 Academic Press.